THERMODYNAMICS 


C.  F.  HIRSCHFELD 

A88T.    PROP.   OF  POWER  .:         I 

CORNELL   UNIVERSITY 


Second  Edition  Revised  and  Corrected 


NEW  YORK 

,  VAN  NO  STRAND  COM  PA  N  V 
23  MURRAY  AND  27  WARREN  STREET* 
1910 


THE 


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ENGINEERING 
THERMODYNAMICS 


C.   F.   HIRSHFELD 

PROFESSOR    OF   POWER   ENGINEERING 
CORNELL  UNIVERSITY 


Second  Edition  Revised  and  Corrected 


NEW  YORK 

D.  VAN  1STOSTRAND  COMPANY 

23  MURRAY  AND  27  WARREN  STREETS 

1910 


COPYRIGHT,  1907 

BY 
D.  VAN  NOSTKAND   COMPANY 


FOREWORD. 


THERMODYNAMICS  is,  like  most  other 
sciences,  built  upon  and  about  a  very 
small  number  of  fundamental  concepts. 
The  average  student,  however,  in  his 
first  attempts  to  obtain  a  working  knowl- 
edge of  this  science  is  staggered  by  the 
enormous  superstructure,  and  fails  to 
observe  and  fix  the  few  fundamentals  upon 
which  that  superstructure  rests. 

The  following  pages  represent  an  at- 
tempt to  develop  the  principal  Thermo- 
dynamic  Properties  of  Gases  and  of 
Vapors  in  such  a  manner  that  the  under- 
lying principles  may  be  clearly  recognized. 
It  is  thought  that  a  thorough  under- 
standing of  the  laws  developed  in  the  text 


360476 


IV 


will,  on  the  one  hand,  give  a  working 
knowledge  sufficiently  extensive  for  most 
engineering  purposes,  or,  on  the  other, 
will  enable  the  student  to  more  easily 
follow  the  generalized  and  complicated 
cases  considered  in  the  large  standard 
works  on  the  subject. 


CONTENTS. 


CHAPTER  I. 

PAGE 

HEAT 1 

CHAPTER  II. 
GASES 18 

CHAPTER  III. 
ENTROPY 44 

CHAPTER  IV.       . 
CYCLES 50 

CHAPTER  V. 
FLOW  OF  GASES 84 

CHAPTER  VI. 
VAPORS 93 

CHAPTER  VII. 
EXPANSIONS  AND  COMPRESSIONS  OF  VAPORS  118 

CHAPTER  VIII. 
VAPOR  CYCLES 127 

CHAPTER  IX. 

FLOW  OF  VAPOR 154 

v 


ENGINEERING  THERMODYNAMICS. 


CHAPTER  I. 
HEAT. 

THE  historical  experiments  of  Rumford 
and  Joule  proved  heat  to  be  a  form  of 
energy;  and  the  work  of  practically  all 
investigators  in  this  field  has  shown  the 
probability  of  heat  being  some  form  of 
molecular  energy;  that  is,  energy  in  some 
way  connected  with  the  motions  and 
positions  of  the  constituent  particles  of 
the  various  masses  with  which  it  is 
associated. 

UNIT  OF  MEASUREMENT. 

Heat  as  a  form  of  energy  may  be 
measured  in  properly  chosen  units  just 


as  any  othev  form  of  energy  may  be 
measured.  In  practically  all  cases  of 
energy  measurement  the  units  are  based 
upon  one  or  more  of  the  effects  produced 
upon  a  given  body  under  given  circum- 
stances by  the  application  of  the  par- 
ticular form  of  energy  considered.  A 
rise  in  temperature  is  one  of  the  most 
noticeable  phenomena  connected  with 
an  increase  of  heat,  and,  since  it  happens 
to  be  an  effect  the  extent  of  which  is 
comparatively  easily  measured,  it  is 
generally  used  as  the  one  upon  which  to 
base  the  measurement  of  heat  energy. 

The  unit  used  by  engineers  in  English- 
speaking  countries  is  called  the  British 
Thermal  Unit  and  is  defined  in  terms  of 
the  amount  of  heat  required  to  cause  a 
unit  temperature  change  in  a  unit  weight 
of  water. 

Thus  the  British  Thermal  Unit  (B.T.U.) 
is  the  quantity  of  heat  required  to  raise 
the  temperature  of  one  pound  of  water 
erne  degree  on  the  Fahrenheit  scale. 

It  has  been  discovered  by  experiment 


that  it  requires  different  amounts  of  heat 
to  produce  this  effect  at  different  initial 
temperatures,  and  the  unit  is  variously 
given  for  different  points  on  the  tempera- 
ture scale.  The  most  common  is  probably 
based  upon  a  change  of  temperature  from 
59°  to  60°.  For  exact  determinations 
this  temperature  rise  should  be  measured 
by  means  of  a  standard  thermometer  with 
gas  for  the  expanding  substarce,  but  for 
all  ordinary  engineering  purposes  measure- 
ments may  be  made  with  a  mercury 
thermometer.  Further,  the  amount  of 
heat  per  degree  per  pound  may,  for  most 
engineering  purposes,  be  considered  con- 
stant at  all  points  of  the  temperature 
scale. 

FIRST  LAW  OF  THERMODYNAMICS. 

Experience  has  shown  that  by  means 
of  proper  apparatus  any  form  of  energy 
can  be  converted  into  other  forms,  and 
that  during  this  process  absolutely  nothing 
is  lost.  Heat  energy  and  mechar.ical 


energy  are  thus  interconvertible  and, 
since  nothing  is  lost  in  the  conversion, 
one  unit  of  the  one  must  always  give  a 
certain  number  of  units  of  the  other. 
The  ratio  of  conversion  has  been  deter- 
mined by  Joule  and  other  experimenters, 
and  the  results  of  their  work  may  be 
expressed  as  a  law;  thus,  Heat  and 
Mechanical  Energy  may  be  converted  the 
one  into  the  other,  and  the  ratio  of  con- 
version is  approximately  one  heat-unit 
to  778  mechanical  units. 
That  is: 

1  B.T.U.  =  778  foot-pounds.        (1) 

The  value  778  is  called  Joule's  equiva- 
lent and  is  represented  by  J.  This  law 
is  generally  called  the  "  First  Law  of 
Thermodynamics." 

It  is  a  very  simple  matter  to  completely 
convert  mechanical  energy  into  heat 
energy,  as  is  exemplified  in  the  heat 
generated  by  friction  of  moving  bodies 
and  in  other  similar  phenomena,  but  the 
change  in  the  opposite  direction  is  by  far 


more  difficult  of  accomplishment.  As 
will  be  seen  later,  the  apparatus  necessary 
to  convert  heat  into  mechanical  forms  of 
energy  is  complicated  and  at  best  does 
not  even  theoretically  convert  all  of  the 
heat  energy  supplied  it.  That  which  is 
converted,  gives  of  course  778  foot-pounds 
per  unit,  but  much  of  it  is  rejected  by 
the  apparatus  still  in  the  form  of  heat, 
and,  what  is  worse,  under  such  conditions 
as  to  be  waste  heat. 

SECOND   LAW  OF  THERMODYNAMICS. 

Study  of  all  the  known  heat  phe:;ome:"a 
of  the  universe  has  shown  that  heat  passes 
readily  from  bodies  of  high  temperature 
to  bodies  of  low  temperature,  but  that 
external  energy  of  some  kind  is  necessary 
to  make  it  pass  in  the  reverse  direction. 
So  important  is  this  fact  that  it  is  called 
the  "  Second  Law  of  Thermodynamics." 

HEAT-ENGINES. 

The  apparatus  previously  mentioned  for 
the  conversion  of  heat  into  mechanical 


forms  of  energy  takes  various  shapes, 
dependent  upon  the  circumstances  of  its 
use,  but  they  may  all  be  called  Heat- 
engines.  They  are  of  particular  im- 
portance in  the  economics  of  this  world, 
because,  while  man  finds  immerse  stores 
of  heat  tied  up  in  latent  form  in  the 
various  fuels  and  easily  liberated  by 
the  chemical  processes  of  combustion, 
the  mechanical  motion  necessary  in  his 
various  industries  does  not  occur  just 
where  and  in  just  the  manner  needed. 
He  is  therefore  driven  by  necessity  to  con- 
vert that  which  he  has  into  that  which 
he  requires  and  he  does  it  in  some  form 
of  heat-engine. 

The  theoretical  performances  of  these 
heat-engines  are  studied  by  means  of  the 
-  laws  of  Thermodynamics,  a  science  built 
upon  the  two  laws  just  given.  It  has  for 
its  object  the  determination  of  all  the 
phenomena  connected  with  the  transfor- 
mations of  heat  into  mechanical  energy 
and  vice  versa.  The  conversion  taking 
place  in  all  heat-engines  depends  upon  the 


behavior  of  various  materials  when  sub- 
jected to  different  kinds  of  heat  treat- 
ment. These  materials  are  called  work- 
ing substances  and  are  usually  contained 
in  some  sort  of  confining  vessels  with 
proper  mechanism  to  transmit  the  motions 
which  they  *  make  available.  They  are 
generally  gaseous  substances  for  practical 
reasons,  though  so  far  as  the  theoretical 
side  of  the  operations  is  concerned  they 
might  be  solid,  liquid,  or  gaseous. 

DISTRIBUTION    OF    HEAT    ENERGY    ASSO- 
CIATED  WITH  ANY  SUBSTANCE. 

It  is  a  matter  of  common  experience 
that  when  substances  are  heated  various 
phenomena  take  place :  temperatures  rise, 
volumes  change,  solids  melt,  liquids 
vaporize,  and  all  sorts  of  other  familiar 
changes  occur.  When  these  are  all  studied 
side  by  side  it  is  found  that  the  results 
of  changing  the  amount  of  heat  associated 
with  any  substance  may  be  grouped  under 
three  heads,  irrespective  of  what  its 


8 


characteristics  are  and  what  changes  it 
may  experience,  provided  it  is  not  set 
in  motion  as  a  whole: 

1.  The  temperature   may  change,   de- 

scribed as  a  change  of  Sensible  Heat. 

2.  Change  may  take  place  within  the 

substance,  necessitating  the  doing 
of  Internal  Work  of  a  positive  or 
negative  character  against  internal 
forces.  This  would  mean  the  ab- 
sorption or  giving  out  of  heat  energy 
equivalent  to  work  represented  by 
the  change. 

3.  The  volume  may  change  with  a  cor- 

responding   displacement     of    the 

surrounding  or  inclosing  medium, 

necessitating  the  doing  of  External 

Work  of    a    positive    or   negative 

character  and  the  transfer  of  an 

equivalent  amount  of  heat. 

These  may  be  easily  pictured  mentally 

if  a  body  of  any  kind  be  assumed  to  be 

made  up  of  molecules  in  rapid  motion  and 

under  certain  circumstances  exerting  some 

sort  of  interattraction.    Then  a  change 


9 


of  temperature  may  be  imagined  as  a 
change  in  the  speed  of  vibration  of  the 
molecules — faster  motion  meaning  higher 
temperature.  An  internal  change  may 
be  imagined  as  a  change  of  distance  be- 
tween the  molecules,  necessitating  a  supply 
of  energy  *to  overcome  their  interattraction 
when  they  are  moved  apart,  and  a  supply 
of  energy  being  liberated  when  they  are 
allowed  to  approach. 

The  change  of  volume  so  far  as  external 
or  enveloping  media  are  concerned  will 
mean  simply  that  these  media  are  dis- 
placed under  whatever  pressure  they 
exert  upon  the  surfaces  of  the  body  chang- 
ing size.  Since  this  means  motion  under 
a  certain  definite  pressure,  work  is  done. 
When  the  motion  is  such  as  to  oppose  the 
pressure,  energy  is  absorbed,  and  energy 
is  liberated  when  motion  is  in  the  same 
direction  as  the  pressures  exerted  by  the 
surrounding  media.  That  is,  when  the 
volume  increases,  energy  is  absorbed  to 
displace  the  enveloping  medium.  When 
the  volume  changes  from  large  to  small, 


10 


energy  is  given  out  to  the  same  extent  as 
it  was  absorbed  at  some  previous  time 
when  the  volume  attained  the  larger  value. 
Since  these  changes  are  due  only  to  the 
change  of  the  amount  of  heat  associated 
with  the  substance,  the  sum  of  all  the 
energy  changes  must  represent  the  amount 
of  heat  charge;  thus,  algebraically, 

Q  =  S  +  I  +  E,  (2) 

where  Q  =  amount    of   heat    absorbed    or 
given  out,  and,  according  to 
the  molecular  theory, 
$=the  amount  of  heat  necessary  to 
make    the    molecules    move 
faster  when  a  rise  in  tempera- 
ture takes  place,  or  the  amount 
given  out  when  their  motion 
becomes  less  rapid  during  a 
drop  of  temperature; 
7= amount  of  energy  absorbed  or 
given  out  by  internal  changes 
of  molecular  distances; 
E  =  amount  of  energy  absorbed  or 
given    out   by    the    external 


11 


media  during  an  increase  or 
decrease  of  the  volume  of  the 
substance  under  considera- 
tion. 

Since  the  amounts  of  energy  represented 
by  S  and  7  are  really  stored  within  a 
substance  when  heated,  the  total  amounts 
of  such  energy  present  in  the  body  are 
called  its  intrinsic  energy.  Then  S+I 
in  a  change  may  be  called  the  change  of 
intrinsic  energy. 

It  should  be  clearly  understood  that 
under  certain  circumstances  all  of  these 
energy  changes  may  not  occur,  while  under 
other  conditions  some  may  be  positive 
while  others  are  negative.  Whatever  the 
conditions,  unless  the  condition  of  motion 
of  the  body  as  a  whole  is  changed,  ex- 
pression (2)  is  always  true  if  the  proper 
signs  and  numerical  values  be  used. 
This  idea  of  the  triple  use  of  heat  will 
become  more  evident  and  take  on  more 
meaning  as  the  subject  is  further  de- 
veloped. 


12 


SPECIFIC   HEAT. 

Equation  (2)  shows  that  if  a  substance 
is  caused  to  undergo  a  certain  change  by 
the  addition  of  heat,  the  amount  of  heat 
required  to  cause  that  change  in  the  same 
body  will  always  be  the  same,  just  as, 
in  any  other  kind  of  a  change  which 
takes  place  in  the  universe,  it  always 
takes  the  same  amount  of  energy  to  do 
the  same  amount  of  work.  It  is  con- 
venient to  have  names  for  the  amounts 
of  heat  required  to  cause  a  unit  amount 
of  change  of  various  kinds,  and  these  are 
called  thermal  capacities.  Thus  there  is 
va  thermal  capacity  for  unit  rise  in  tem- 
perature, and  this  is  commonly  called  the 
Specific  Heat.  Similarly,  there  is  a 
thermal  capacity  for  unit  change  of  volume 
and  it  is  commonly  called  the  Latent  Heat 
of  Expansion.  There  are  several  other 
thermal  capacities,  but  they  are  of  minor 
importance  and  have  no  commonly  ac- 
cepted names. 

As  just  indicated,  the  Specific  Heat  of  a 


13 


body  is  the  amount  required  to  cause  unit 
temperature  change  in  unit  weight,  and, 
if  the  specific  heat  is  constant  at  all 
temperatures, 

SrT=C,  (3) 


where  T%  and  T\  represent  final  and  initial 

temperatures; 

W= weight  of  substance  in  pounds; 
and       C= Specific  Heat. 

This  expression  may  be  written 

Q  =  C7TF(r2-r1);  (4) 

and  if  the  specific  heat  is  variable,  then 

/"  T 

Q=W        *CdT.  (5) 

J*v 

From  equation  (2)  it  can  be  seen  that 
it  would  be  possible  for  Q  to  have  different 
values  for  the  same  change  in  tempera- 
ture if  that  temperature  change  could  be 
accompanied  by  different  amounts  of 
internal  and  external  work.  Therefore 


14 


in  equation  (4)  the  value  of  C  may  vary 
with  the  conditions  of  heating;  that  is, 
the  value  of  the  specific  heat  may  vary 
according  to  the  conditions  of  heating, 
and  every  substance  may  have  several 
specific  heats.  This  is  actually  the  case, 
as  will  be  shown  in  the  development  of 
the  equations  for  the  behavior  of  gases. 

Of  all  the  numerous  possible  values  for 
the  specific  heat  of  any  single  substance, 
it  would  seem  possible  to  find  one  which 
represented  the  heat  necessary  to  cause  a 
change  in  S  only.  That  is,  one  which 
represents  the  quantity  of  heat  necessary 
to  cause  a  change  of  temperature  without 
any  other  heat-absorbing  phenomena. 
Such  a  one  would  be  called  the  True 
Specific  Heat  and  would  represent  only 
the  heat  necessary  to  increase  the  velocity 
of  vibration  of  the  molecules  during  a  rise 
in  temperature  of  one  degree.  Such  a 
specific  heat  will  be  considered  in  dealing 
with  gases. 


15 


EXTERNAL  WORK  DURING  VOLUME  CHANGES. 

It  is  often  necessary  or  desirable  for 
purposes  of  analysis  to  divide  the  heat 
associated  with  changes  in  the  condition 
of  a  bocly;  that  is  to  say,  how  much  of 
it  represents  change  of  sensible  heat,  how 
much  represents  internal  work,  and  how 
much  external  work.  For  this  purpose 
an  expression  for  the  value  of  the  external 
work  is  very  necessary,  and  such  an  ex- 
pression may  be  easily  developed. 

Assume  any  substance  enclosed,  as  in 
Fig.  1,  in  the  end  of  a  cylinder  behind 


FIG.  1. 


a  moving  piston   of   area  a  square  feet 
and  under  a  pressure  of  P  pounds  per 


16 


square  foot.  If  the  body  be  allowed  to 
expand  while  the  pressure  is  maintained 
constant,  it  will  drive  the  piston  out 
through  a  distance  which  may  be  called 
L  feet.  The  expanding  substance  will 
the  i  be  doing  external  work,  that  is, 
work  upon  the  confining  piston,  and  the 
value  of  the  external  work  in  B.T.U. 
will  be 

aPL 


but  aL  is  the  volume  through  which  the 
piston  moves,  that  is,  the  change  of  volume 
of  the  expanding  substance,  and  if  V\ 
and  72be  initial  and  final  volumes  in  cubic 
feet, 

P(F2-y!) 

E=    -778—  ' 
Similarly,  if  the  pressure  be  variable, 


each  infinitesimal  volume  change  being 
multiplied  by  the  pressure  existing  while 
it  took  place  and  then  all  the  small  values 
of  E  being  added  together. 


17 


It  is  readily  seen  that  equations  (6) 
and  (7)  will  apply  equally  well  to  cases 
where  the  volume  change  takes  place  in 
all  three  possible  directions  and  they  are 
therefore  expressions  for  external  work 
done  during  any  kind  of  volume  changes. 


CHAPTER  II. 
GASES. 

EXPERIMENTAL  investigations  into  the 
behavior  of  gases  under  different  condi- 
tions show  that  they  all  approximately 
obey  very  simple  laws.  None  of  them 
exactly  obey  these  laws,  but  the  farther 
the  gases  are  removed  from  their  points 
of  liquefaction  the  nearer  do  the  laws 
express  their  characteristics.  Such  being 
the  case,  it  has  become  customary  to 
consider  an  ideal  " Perfect  Gas"  and  to 
develop  the  laws  which  it  would  obey, 
and  then  so  far  as  necessary  to  study  the 
variations  of  the  real  gases  from  those 
laws.  For  all  practical  engineering  pur- 
poses all  of  the  ordinary  so-called  "  per- 
manent gases  "  may  be  assumed  as  perfect 
gases. 

18 


19 


LAWS  OF  THE  PERFECT  GAS. 

A  Perfect  Gas  may  be  defined  as  a 
substance  existing  in  such  a  physical 
state  that  its  constituent  particles  (mole- 
cules) exert  no  interattraction.  Such  a 
body  would  perfectly  obey  the  laws  of 
Boyle  and  Charles. 

Boyle's  Law  states  that  when  the  tem- 
perature of  a  gas  is  constant,  its  volume 
mill  vary  inversely  as  the  pressure  upon  it; 
that  is, 

%-%• 

or  ViPi  =  P2V2  =  Si  constant.         (9) 

Charles'  Law  states  that  with  the  pressure 
or  the  volume  constant,  the  volume  or  the 
pressure  of  a  gas  will  vary  ±1-$  of  its  volume 
at  32°  F.  for  every  Fahrenheit  degree  change 
of  temperature,  increasing  in  volume  or 
pressure  when  the  temperature  increases. 
If  a  gas  be  imagined  with  unit  volume  at 
32°  F.,  it  would  lose  T£¥  part  of  that 
volume  for  every  degree  drop  in  tempera- 


ture  at  constant  pressure,  and  when  it  had 
dropped  493  degrees  it  would  have  zero 
volume  if  the  law  held  at  such  low  tem- 
peratures. 

Such  a  point  on  the  temperature  scale, 
which  is  (493-32  =  )  461  degrees  below  the 
Fahrenheit  zero,  is  called  the  Absolute 
Zero,  and  temperatures  measured  from  it 
are  called  Absolute  Temperatures.  If  the 
absolute  temperature  be  represented  by 
T,  Charles'  Law  may  be  very  simply 
stated  in  algebraic  form: 

When  pressure  is  constant, 

£=£;  do) 

\2      *2 

When  volume  is  constant, 

"rr==T>~~*  (1-U 

JT2       ±2 

This  idea  of  absolute  temperature  is 
very  useful  in  dealing  with  heat-engines. 
The  absolute  temperature  of  a  body  in 
Fahrenheit  degrees  may  be  obtained  from 


21 

the  ordinary  temperature  above  Fahren- 
heit zero  by  adding  461 : 

!F  =  *.+  461.  (12) 

Apparently  if  real  gases  obey  the  law 
of  Charles,  they  would  have  no  volume 
at  the  temperature  of  absolute  zero,  but 
this  absurdity  need  not  be  considered 
because  they  would  all  liquefy  before 
reaching  such  a  low  temperature.  That 
is,  they  would  cease  to  even  approxi- 
mately obey  the  law  which  leads  to  this 
absurdity. 

Boyle's  and  Charles'  Laws  may  be  com- 
bined to  give  a  third  and  more  general 
Law  of  Perfect  Gases.  If  a  volume  of 
gas,  Vi,  at  pressure  PI  and  temperature 
TI  have  its  temperature  maintained 
constant  while  its  pressure  is  changed  to 
P',  its  new  volume,  V,  will  be  given  by 
equation  (8): 

F'=^.  (13) 

If  then  its  pressure  be  kept  constant 
while  its  temperature  is  varied  to  T2, 


22 


its  new  volume,  V2>  will  be  given  by  equa- 
tion (10)  : 


and  substituting  for  V  from  (13), 


Since  Pr  is  the  same  as  P2,  an  expres- 
sion is  derived  which  gives  the  value  of 
the  volume  change  for  variations  of 
both  temperature  and  pressure: 


—— 
2  --  p  T    , 

-TV  1 

which  may  be  written 

P  V      P  V         PV 

-jr^  •  =-|r-^  or  -^-=a  constant.  (17) 

Where  the  value  of  V  above  is  for  one 
pound  of  gas,  the  constant  is  called  R, 
and  this  gives 

PV 

~r=R.  (18) 


23 


Any  of  the  equations  under  (17)  or  (18) 
is  called  the  Law  of  Perfect  Gases. 


SPECIFIC  HEAT  OF  PERFECT  GASES. 

A  material  constituted  as  is  this  ideal 
gas  offers  absolutely  no  resistance  to  sepa- 
ration of  'its  constituent  particles,  since 
they  exert  no  attraction  upon  one  an- 
other, and  therefore  when  it  is  heated  no 
energy  is  absorbed  for  the  purpose  of 
doing  internal  work. 

Hence  in  this  case  one  pound  of  mate- 
rial when  heated  would  require  an  amount 
of  heat 

(19) 


If  such  material  is  heated  at  constant 
volume,  the  pressure  rises  directly  as  the 
absolute  temperature,  as  shown  by  the 
law  of  perfect  gases,  but  no  external  work 
is  done  because  the  enveloping  medium 
is  not  displaced  ,  and  under  such  condi- 
tions 

Q=S.  (20) 


24 


In  such  a  case  the  "  Real  or  True  "  Specific 
Heat  can  be  found  by  dividing  Q  by  the 
change  of  temperature,  provided  that 
specific  heat  is  constant  with  variable 
pressure  and  variable  temperature.  If  it 
varies,  the  quotient  will  only  be  the 
average  real  specific  heat. 

The  specific  heat  obtained  under  the 
conditions  of  constant  volume  as  above 
is  designated  by  Cv  when  expressed  in 
Thermal  Units,  and  by  Ky  when  ex- 
pressed in  foot-pounds.  Then 


(21) 


In  the  case  of  the  ideal  gas  there  is  no 
theoretical  reason  why  C*  should  not  be 
constant,  that  is,  why  it  should  not  re- 
quire exactly  the  same  amount  of  heat 
to  raise  the  temperature  of  one  pound  of 
a  given  gas  one  degree  with  volume  con- 
stant no  matter  what  the  temperature, 
pressure,  and  volume. 

If  this  quantity,  Cv,  obtained  by  di- 
viding S  by  the  change  of  temperature  of 


25 


the  body  while  receiving  heat  S,  is  a 
constant,  it  follows  that  the  total  sensible 
heat  or  intrinsic  energy  possessed  by  a 
gas  must  depend  upon  its  temperature 
only.  Thus  if  a  gas  have  its  tempera- 
ture increased  n  degrees,  its  intrinsic 
energy  will  have  been  increased  by  nCv 
heat-units,  and  if  it  have  its  temperature 
increased  nf  degrees,  its  sensible  heat  or 
intrinsic  energy  is  increased  by  n'Cv 
heat-units.  That  the  intrinsic,  energy  of 
real  gases  may  be  considered  to  depend 
upon  temperature  only,  and  to  be  inde- 
pendent of  volume  and  pressure,  is  shown 
by  an  experiment  devised  and  performed 
by  Joule  and  Thomson. 

Their  experiment  was  performed  by 
means  of  two  vessels  connected  by  a 
passage  containing  a  valve.  One  vessel 
was  filled  with  gas  at  high  pressure  and  the 
other  wras  devoid  of  material  content, 
that  is,  contained  a  vacuum.  These  two 
vessels  were  immersed  in  a  larger  vessel 
containing  water,  and  when  everything 
had  reached  the  same  temperature,  the 


26 


valve  between  the  two  was  opened  so 
that  the  gas  expanded  in  volume  until 
it  filled  both  vessels  at  an  equal  but 
lower  pressure.  Thermometers  stowed 
that  no  heat  was  given  to  or  taken  from 
the  surrounding  water,  that  is,  the  gas 
neither  lost  nor  gained  energy,  and  that 
after  equilibrium  had  been  established 
the  temperature  of  the  gas  within  the  two 
vessels  was  sensibly  what  it  had  been 
when  occupying  only  one  vessel  at  a  higher 
pressure. 

Here,  then,  was  a  change  of  pressure  and 
volume  with  no  loss  or  gain  of  heat  energy 
by  the  gas  within  the  vessel  and  the  tem- 
perature remaining  constant.  It  should 
be  noted  that  no  energy  could  have  been 
lost  by  the  doing  of  external  work  because 
under  the  circumstances  the  gas  could  do 
none.  It  therefore  requires  exactly  the 
same  amount  of  sensible  heat  or  intrinsic 
energy  to  maintain  a  certain  temperature 
no  matter  what  the  pressure  and  volume, 
and  therefore  the  intrinsic  energy  of  a  gas 
may  be  said  to  depend  upon  the  tempera- 


27 


ture  only  and  to  be  independent  of  pressure 
and  volume. 

In  describing  this  experiment  the  tem- 
perature before  and  after  expansion  was 
said  to  be  "  sensibly  the  same/7  and  ad- 
visedly. Very  accurate  measurements 
showed  slight  variations  of  temperature 
with  the  different  gases  tested,  because 
in  actual  gases  the  molecules  do  exert 
interattractions.  The  experiments  when 
considered  with  others  of  similar  nature 
indicated,  however,  that  these  tempera- 
ture changes  would  disappear  when  the 
attractions  disappeared. 

If  one  pound  of  gas  be  heated  in  such 
a  way  that  the  pressure  remains  constant, 
the  volume  increases  directly  as  the 
absolute  temperature,  T.  Increase  of 
volume  under  external  pressure  means  the 
doing  of  external  work,  and  the  heat 
necessary  to  cause  a  change  of  tempera- 
ture under  these  conditions  will  be 

Q  =  S+E.  (22) 

For    a   given    temperature    range    the 


28 


specific  heat  may  be  found  by  dividing 
Q  by  the  temperature  range,  providing 
that  specific  heat  be  constant.  If  it  is  not 
constant,  the  quotient  as  before  would 
be  its  average  value  through  the  particular 
temperature  range  chosen.  The  specific 
heat  under  constant  pressure  conditions 
is  designated  by  Cp  when  measured  in 
thermal  units,  and  by  Kp  when  measured 
in  mechanical  units.  Then 

77SCP=KP.  (23) 

Since  the  value  of  Q  given  by  equation 
(22)  is  larger  than  the  value  of  Q  given 
by  equation  (20)  by  just  the  amount  of 
the  external  work  done,  it  is  immediately 
seen  that  the  specific  heat  at  constant 
pressure  is  greater  than  the  specific  heat 
at  constant  volume  by  the  amount  of  ex- 
ternal work  done  by  volume  increase  in 
the  first  case.  This  is  easily  seen  to  be 
so  by  imagining  a  change  of  one  degree 
-in  temperature  under  the  two  different 
conditions.  Then  if  the  material  being 
heated  weighs  exactly  one  pound,  the 


29 

quantity  of  heat,  Q,  is  the  specific  heat 
in  each  case. 

CP  —  CV  =  E  expressed  in  thermal  units  (24) 
and 

VVi).      (25) 


The  fact  that  Cp  may  be  taken  as  prac- 
tically constant,  that  is,  independent  of 
the  pressure,  for  the  ordinary  gases  has 
been  proved  by  experiment,  and  it  can 
readily  be  seen  that  it  must  be  constant 
for  the  perfect  gas  by  the  following  line 
of  reasoning. 

Cp  is  larger  than  the  constant  Cv  by 
just  the  amount  of  the  external  work  done 
during  a  change  of  temperature,  and  since 
the  value  of  Cv  is  the  same  for  any  o::e 
particular  gas  no  matter  what  the  pressure, 
the  value  of  Cp  must  be  independent  of 
the  pressure  if  it  can  be  shown  that  the 
external  work  done  in  raising  the  tem- 
perature from  a  value  T\  to  a  value  T% 
is  the  same  at  any  two  different  pressures. 


30 

If  a  pound  of  gas  b.e  assumed  to  nave 
a  volume  V\  at  pressure  PI  and  tem- 
perature T7!,  and  to  have  a  volume  V\ 
at  pressure  P\  but  the  same  temperature 
TI,  and  if  in  both  cases  the  temperature 
be  raised  to  T2  while  the  pressure  remains 
constant,  Boyle's  Law  gives 

PI  Vi  =  Pi'VV  at  temperature  Tl ,     (27) 
and 

Pi72  =  Pi/72/  at  temperature  T2.     (28) 
If  now  (27)  be  subtracted  from  (28), 

Pi(V2-V1)  =  Pl'(V2'-Vi');        (29) 

shov.ing  the  external  work  to  be  the  same 
in  each  case.  It  is  therefore  independent  of 
-  the  pressure  during  the  change,  provided 
that  pressure  is  constant  and  depends 
only  on  the  value  of  the  initial  and  final 
temperatures.  It  therefore  follows  that 
the  value  of  Cp  is  independent  of  the 


31 


pressure  and  is  a  constant  for  a  perfect 
gas. 

RELATIONS    EXISTING    BETWEEN    SPECIFIC 
HEATS. 

Returning  to  equation  (25)  for  a  change 
of  temperature  cf  one  degree, 


KP-KV=          PdV, 
JVi 

and  for  any  change  of  temperature 


rv2 
/     PdV,      (30) 

JVi 


which  for  constant  pressure  changes  is, 
by  equation  (6), 

Kp(T2-Tl)-Kt(T2^Tl) 

=Pi(V2-Vi).     (31) 

From  equation  (18), 
PlVl  =  RlTl    and    P2V2=RT2, 


32 


and   when   Pi=P2,    that   is,   when   the 
pressure  during  a  -change  is  constant, 


so  that  (31)  may  be  written 

KP-KV  =  R;  (32) 

showing  that  R,  the  constant  in  the 
perfect-gas  law,  is  really  the  value  of 
the  external  work  done  by  one  pound  of 
gas  when  undergoing  a  change  of  tem- 
perature of  one  degree  at  constant  pres- 
sure. 
In  many  cases  the  ratio  of  the  two 

-rr 

specific  heats  ~  occurs,  and  this  is  repre- 
A,, 

sented  by  ?.    Writing  (32) 
Kv  =  Kp—  R, 

a    useful    expression    in    terms    of    Kv, 
R,  and  7-  may  be  obtained  by  dividing 


33 

by  Kv,  substituting  j-  for  ^-p,  and  trans- 
posing.    This  gives 

R 


TYPE  VOLUME  CHANGES. 

The  facts  so  far  developed  may  now 
be  made  use  of  .in  deriving  the  laws 
governing  expansions  and  compressions 
of  gases.  By  expansion  is  meant  an  in- 
crease of  volume,  and  by  compression  is 
meant  a  decrease  of  volume.  There  are 
an  infinite  number  of  possible  expansions 
and  compressions  dependent  upon  different 
laws  of  heat  change,  but  two  are  of  par- 
ticular importance  in  the  study  of  heat- 
engines. 

These  are  called 

(a)  Isothermal  volume  changes,  and 

(6)  Adiabatic  volume  changes. 

Isothermal    changes    are    those    taking 


place  while  the  temperature  remains  con- 
stant. 

Adiabatic  changes  are  those  taking  place 
without  reception  or  rejection  of  heat,  as 
heat,  by  the  body  changing  volume. 


ISOTHERMAL  VOLUME  CHANGES. 

An  isothermal  change  is  easily  analyzed 
by  means  of  Boyle's  Law,  equation  (9). 
If  the  temperature  remains  constant, 


constant. 


Plotting  this  equation  with  horizontal 
distances  equal  to  volumes,  and  vertical 
distances  equal  to  pressures,  a  curve  is 
obtained  as  shown  in  Fig.  2.  The  law 
of  expansion  may  be  regarded  as  a 
logarithmic  equation  of  the  form 

P7n=a  constant, 
in  which  n  is  equal  to  unity. 


35 


//  external  work  is  done  during  an  isother- 
mal increase  of  volume,  an  amount  of  heat 
energy  equal  to  the  work  done  must  be 


Volume 


FIG.  2. 

consumed.  Since  the  expanding  gas  by 
definition  is  maintained  at  constant  tem- 
perature, the  work  cannot  be  done  at  the 
expense  of  its  own  intrinsic  energy.  The 


36 


only  alternative  is  that  heat  equal  in  amount 
to  external  work  done  be  supplied  from  some 
outside  source.  Equation  (18)  shows  that 
if  the  temperature  of  a  gas  remains  con- 
stant, the  pressure  must  decrease  in  pro- 
portion to  the  increase  of  volume.  The 
external  work  can  then  be  expressed  by 
equation  (6): 


and  since 

PI  V\  =  P7=  a  constant, 

equation  (34)  may  be  written 

rv*P,V,  fVidV 

778E-/      Z£ldV-.plVl          % 

i/F,  JVl        V 

integrating  which  gives 

77SE=P1V1  (log.  F2-loge  Fj) 


(log.  I?). 


(35) 


37 


Calling  ~  the  ratio  of  expansion,  r, 

778E=P1  Vi  log*  r=RTl  loge  r,       (36) 

and   the   heat   supplied   during   the   ex- 
pansion will   be 


!  FT  loge  r     RT^  loge  r 

~778~~          ~~~ 


If  a  decrease  of  volume,  that  is,  a  com- 
pression, be  considered,  an  amount  of  work 
equal  to  that  shown  in  equation  (36) 
would  have  to  be  expended  upon  the  gas, 
and  an  equal  amount  of  heat  would  be 
generated  which  in  some  way  would 
have  to  be  carried  off  by  external  means 
to  keep  the  temperature  constant. 

ADIABATIC  VOLUME  CHANGES. 

In  the  case  of  an  Adiabatic  Expansion 
any  work  done  by  an  increase  of  volume 
would  have  to  be  done  at  the  expense  of 
heat  already  contained  within  the  expanding 


38 


gas,  because  during  such  an  expansion  no 
heat  can  be  received  from  external  sources. 
That  is,  the  work  would  be  done  at  the 
expense  of  its  intrinsic  energy  and  therefore 
its  temperature  would  drop.  Experience 
has  shown  that  an  adiabatic  expansion  can 
be  represented  by  the  same  form  of  loga- 
rithmic equation  as  that  used  for  the 
isothermal;  in  this  case,  however,  n 
would  have  a  different  value. 

pl  Vt*  =  P2V2n  =  PVn  =  a  constant    (38) 

may  then  be  taken  as  the  equation  of 
adiabatic  expansion. 
The  external  work  would  be,  as  before, 


=  fV 
Jv, 


and  substituting  from  (38), 


39 


integrating  which  gives 


Pi  FiVa—      i 

778E=lVl  (\_n      l  (39) 

which  by  means  of  equation  (38), 

Pl 

can  be  written 


'.    (40) 
n-l  n-l 

Since  the  amount  of  external  work 
done  must  be  equal  to  the  change  of 
intrinsic  energy,  and  since  in  a  perfect 
gas  this  is  equal  to  the  change  of  sensible 
heat,  S,  it  follows  that 


2  ,.1N 

t,  :  -  >        (41) 

71       1 

and  substituting  for  Kv  by  means  of  (33), 

R(Tl-T2)  _R(T1-T2) 
7—1  n-l 

which  shows  that  for  adiabatic   expan- 
sion of  a  perfect  gas 


40 
and  the  equation  for  such  an  expansion  is 


PiVlr=P2V2r  =  PVr  =  const.  (43) 
The  work  being  done  at  the  expense  of 
sensible  heat,  there  must  be  a  drop  of 
temperature,  and  this  can  be  found  by 
combining  equation  (43)  with  the  law 
of  perfect  gases,  equation  (17).  These 
two  give 

w_ 
~ 


which  multiplied  together  and  simplified 
give 

Il-(Y*\-1',  (44) 

1*1"  w 

and  representing  ratio  of  expansion  by  r, 
^  =  r-1.  (45) 

^2 

It  is  often  convenient  to  have  the  ratio 
of  the  temperatures  expressed  in  terms 
of  the  pressures,  and  this  can  easily  be 

done  by  substituting  for  (T^)  in  equa- 


41 


tion  (44)  its  value  derived  from  equation 
(43),  giving 


Adiabatic  Compressions  are  the  exact 
reverse  .of  adiabatic  expansions.  The 
work  expended  by  external  bodies  to 
compress  the  gas  will  all  be  converted 
into  sensible  heat  in  the  gas,  since  by 
definition  none  can  be  given  out  by  the 
material  under  compression.  Such  being 
the  case,  there  will  be  a  rise  of  tempera- 
ture equal  to  the  drop  during  expansion 
between  corresponding  volume  limits. 
The  equations  previously  developed  for 
external  work  done  by  the  gas  during 
expansion  also  give  the  value  of  work 
done  upon  the  gas  during  compression. 

AREA    AS    MEASURE    OF    EXTERNAL    WORK. 

It  has  been  shown  that  both  Isothermal 
and  Adiabatic  changes  may  be  represented 
by  means  of  the  general  equation 

plVln  =  P2V2n  =  PVn  =  a  constant, 


42 


and  that  the  external  work  in  each  case 
can  be  represented  by  the  equation 

77SE  =   fV*PdV. 

Such  volume  changes  may  be  plotted  to 
PV  coordinates  and  give  curves  of  ap- 
proximately similar  appearance,  though 
with  sl'ghtly  different  curvatures  and 
slopes.  For  the  following  demonstration 
the  curve  of  Fig.  3  may  be  assumed  to 
represent  any  such  volume  change. 

Since  the  area  abed  under  this  curve  is 

A=    fV2PdV, 
Jvl 

and  since  this  is  the  same  as  the  expression 

A=77SE.  (47) 

That  is,  the  area  under  a  curve  0:1  a  PV 
diagram  represents  external  work  done 
by  a  body  expanding  according  to  the 
law  represented  by  that  curve,  or  repre- 
sents work  done  upon  a  body  compressed 
according  to  the  same  law. 


43 


In  the  case  of  isothermal  expansion 
this  area  must  then  equal  the  heat  sup- 
plied from  external  sources  during  ex- 


FIG.  3. 

pansion,  and  in  the  case  of  adiabatic 
expansion  it  must  represent  the  loss  of 
intrinsic  energy. 


CHAPTER  III. 
ENTROPY. 

IN   dealing  with  heat-engines  the  ex- 
pression — ,  or  the  change  of  quantity 

of  heat  divided  by  the  absolute  tempera- 
ture at  which  the  change  takes  place,  is 
of  very  frequent  occurrence  and  has 
received  a  name.  This  expression  is  said 
to  represent  the  change  of  Entropy  of 
the  body.  If  Entropy  be  denoted  by  <£, 

d^,  (48) 

and 

dQ=Td<f>,  (49) 

which  may  be  integrated  as  indicated  in 
the  following  equation: 

Td<f>.          (50) 

01 
44 


45 


It  can  easily  be  seen  from  equation  (49) 
above  that  the  entropy  of  a  body  must 
increase  when  heat  is  added  to  it  and 
decrease  when  heat  is  taken  from  it, 
and  therefore  remain  constant  when  no 
heat  is  received  or  rejected. 

ENTROPY  DIAGRAMS. 

If  coordinates  be  chosen  with  vertical 
distances  representing  absolute  tempera- 
ture and  horizontal  distances  representing 
entropy,  it  is  possible  to  plot  the  various 
entropy  changes  which  bodies  undergo 
when  subjected  to  heat  treatment. 

Thus  in  the  case  of  an  isothermal  ex- 
pansion the  temperature  remains  constant, 
and  hence  the  line  representing  such  a 
change  upon  the  entropy-temperature 
diagram  must  be  horizontal  as  in  Fig.  4. 
Heat  having  been  added  to  the  body  at 
constant  temperature,  the  entropy  has 
increased. 

During  an  adiabatic  expansion  no  heat 
is  received  or  rejected,  and  therefore  the 


46 


entropy  must  remain  constant,  that  is? 
the  line  representing  such  change  must  be 
vertical  as  in  Fig.  4.  This  shows  a  drop 


Is 

sothermal  Cha 

age 

0 

50 

a 

<D 

§ 

I 
o 

£ 

o 

2 

I 

Adiaba 

Entropy 

FIG.  4. 


in  temperature  such  as  actually  occurs 
during  adiabatic  expansion,  or  a  rise  in 
temperature  for  adiabatic  compression. 


47 


ENTROPY  CHANGES. 


In  the  case  of  Isothermal  Expansion, 
equation  (50), 


becomes 

&),          (51) 


since  the  temperature  is  constant. 

In  the  case  of  Adiabatic  Expansion,  no 
heat  being  received  or  rejected, 


Q2-Qi= 

and  therefore 


(52) 


Thus  the  area  under  a  line  on  the  T(j> 
diagram  represents  the  heat  change;  area 
under  a  line  traced  from  left  to  right 
represents  heat  supplied  to  the  body, 
and  under  a  line  traced  from  right  to  left, 
heat  rejected  by  the  body. 


48 


In  a  general  case  of  heat  change  of  any 
kind,  equation  (48), 


may  be  written 

CdT 


where  C  represents  the  proper  specific 
heat  for  the  conditions  governing  the 
heat  change.  If  C  be  assumed  constant, 
integration  gives 


=  Clogep,          (53) 
-*  i 

so  that  the  total  change  of  entropy  for  a 
given  temperature  change  can  be  cal- 
culated whenever  the  proper  value  of  the 
specific  heat  is  known. 

The  change  of  entropy  of  a  perfect  gas 


49 


when  being  heated   or  expanded   under 
'  constant  pressure  is  then 

<£2-<£i=Cploge~-2,  (54) 

and  when  being  heated  at  constant  volume 

f*-*i-G*ia*r.  (55) 


CHAPTER  IV. 
CYCLES. 

THE  working  substances  of  heat-engines 
are  generally  in  theory  carried  through 
some  sort  of  a  series  of  changes  in  such  a 
way  that  they  periodically  return  to  a 
certain  set  of  initial  or  starting  conditions. 
Such  a  series  of  changes  form  what  is  known 
as  a  thermodynamic  cycle. 

The  most  interesting  of  these,  both 
historically  and  thermodynamic  ally,  is 
the  so-called  "  Cycle  of  Carnot/'  or 
simply  "Carnot  Cycle."  It  could  be 
carried  out  with  any  material  for  working 
substance,  but  will  be  investigated  here 
for  the  case  of  a  perfect  gas  only. 
50 


51 


THE   CAHNOT   CYCLE. 

For  the  generation  of  the  Carnot  cycle 
several  more  or  less  ideal  pieces  of  appara- 
tus are  necessary: 

1.  A    cylinder    and    frictionless    piston 

made  of  a  material  which  is  a  per- 
fect non-conductor  of  heat. 

2.  A  perfectly  conducting  end  or  cover 

for  that  cylinder  and  another  cover 
of  non-conducting  material  which 
may  be  made  to  fit  over  the  first. 

3.  A  hot  body  so  arranged  as  to  main- 

tain a  constant  temperature,  T\, 
no  matter  how  much  heat  be  taken 
from  or  added  to  it. 

4.  A  cold  body  arranged  to  maintain  a 

constant  temperature,  TV 

5.  A  working  substance  enclosed  within 

the  cylinder. 

Assuming  one  pound  of  perfect  gas  for 
simplicity,  imagine  it  enclosed  within 
the  cylinder  between  head  and  piston  and 
having  volume  and  pressure  as  shown  at 
a  in  Fig.  5.  Assume  its  temperature 
equal  to  TV 


52 


FIG.  5. 


53 


Then  if  the  hot  body  at  temperature  T\ 
be  brought  in  contact  with  the  perfectly 
conducting  cylinder  end,  the  gas  may  be 
allowed  to  expand  isothermally,  driving 
out  the  piston,  and  receiving  any  heat 
necessary  from  the  hot  body  at  a  tem- 
perature T\.  Assume  this  expansion  to 
continue  from  VaPa  conditions  to  F&P& 
conditions,  and  then  the  hot  body  to  be 
removed  and  the  cylinder  end  protected 
by  the  non-conducting  cover.  If  ex- 
pansion continues  under  these  conditions, 
the  body  is  insulated  from  heat  transfer 
and  therefore  the  change  will  be  adiabatic. 
Assume  the  expansion  to  continue  to  VCPC 
conditions,  at  which  point  the  tempera- 
ture has  dropped  to  7^,  the  temperature 
of  the  cold  body.  If  now  the  protecting 
cover  be  removed,  the  cold  body  be  brought 
in  contact  with  the  cylinder,  and  the 
piston  forcibly  driven  in,  the  resulting 
compression  would  be  isothermal  at  a 
temperature  T%.  The  heat  generated  by 
that  compression  would  be  absorbed  by 
the  cold  body  at  the  low  temperature  772. 


54 


Imagine  this  compression  stopped  at  a 
properly  chosen  point,  d,  so  that  adia- 
batic  compression  from  that  point  would 
bring  the  body  back  to  initial  conditions 
PaVa-  At  the  time  conditions  PdVd 
are  arrived  at,  remove  the  cold  body, 
replace  the  protecting  cover,  and  then 
continue  the  compression  until  the  PaVa 
conditions  are  again  attained.  The  tem- 
perature would  rise  because  of  the  work 
done  upon  the  gas  during  compression, 
and  when  PaVa  conditions  were  reached 
the  gas  would  have  to  have  the  same  tem- 
perature as  it  had  to  start  with,  namely, 
T\.  Therefore  the  cycle  would  be  com- 
plete. 

Since  the  areas  as  cross-hatched  under 
curves  ab  and  be  would  represent  external 
work  done  by  the  gas,  and  the  areas 
under  cd  and  da  work  done  upon  the  gas, 
the  net  result  of  the  operation  would  be 
the  work  represented  by  the  area  abed 
or  that  enclosed  by  the  four  lines  of  the 
cycle. 

If  efficiency  be  defined  as 


Eff.= 


55 

Useful  result 


Expenditure  made  to  obtain  that  result 
Result  (56) 


Effort ' 

the  efficiency  in  this  case  would  be 
Useful  external  work 


Eff.= 


Heat  suppl'd  from  hot  boay  to  do  that  work 
__  _  Area  abed  in  foot-pounds 
Heat  from  hot  body  in  foot-pounds* 

Since  the  total  amount  of  energy  made 
available  in  mechanical  form  must  equal 
the  amount  of  heat  energy  which  has 
disappeared,  the  expression  for  efficiency 
may  be  still  further  simplified  as 


_Heat  supplied  —  Heat  rejected 
Heat  supplied 


(57) 


It  is  evident  that  in  the  expression  for 
efficiency  the  heat  which  is  rejected  can- 
not be  credited  to  the  engine  because 
its  temperature  is  so  low  that  it  cannot 
again  be  used  in  that  engine. 


56 


The  operations  taking  place  during  this 
cycle  may  be  analyzed  by  means  of  the 
equations  already  developed  for  gases, 
and  the  results  may  be  tabulated  as 
below : 

Line.  Heat  received.  Work  done. 

ab         +  RTl  log,  r          +  RTl  log,  r 
lc  0 


n— 1 

cd         -  RT2  log,  r'          -  RT2  log,  r' 

da  0 

n  —  l 

The  value  of  r'  in  this  table  can  be 
shown  equal  to  r  as  follows: 

The  drop  of  temperature  during  the 
adiabatic  expansion  is  given  by 

r-l 


and  the  rise  of  temperature  during  the 
adiabatic  compression  is  given  by 


57 
so  that 

n~v, 

and 

Vm~f*' 

giving      • 

r=r'. 

Writing  efficiency 

Pff  _  Net  external  work 
Heat  supplied     ' 

the  tabulated  values  give 

Vff  _^^i  l°ge  r  —  RT2  loger 
RTi  loge  r 

=  ^F^-2'  (58) 


This  result,  which  is  dependent  upon 
temperatures  only,  is  known  as  the  Carnot 
Efficiency.  It  is  interesting  to  note  that 
the  efficiency  of  transformation  of  heat 
into  mechanical  energy  increases  as  the 


58 


temperature  difference  increases,  and  can 
never  equal  unity  or  100%  unless  T2  is 
equal  to  absolute  zero. 

As  will  be  shown  in  the  succeeding 
paragraphs,  no  heat-engine  can  be  con- 
structed which  is  more  efficient  than  the 
Carnot,  and  hence  no  engine  can  be 
expected  to  have  even  a  theoretical  effi- 
ciency of  100%  under  ordinary  circum- 
stances. 

REVERSED    HEAT-ENGINES. 

There  is  no  reason  why  the  Carnot 
cycle  as  just  studied  could  not  be  carried 
through  in  the  reverse  direction.  That 
is,  starting  at  a,  allow  adiabatic  expansion 
to  d,  then  isothermal  expansion  in  con- 
tact with  cold  body  at  temperature  T2 
until  the  point  c  is  reached,  then  compress 
adiabatically  to  b  and  then  isothermally 
to  a.  The  results  of  such  a  serifes  of 
operations  would  be  just  the  reverse  of 
those  in  the  first  case.  When  carried 
through  in  a  clockwise  direction  the  cycle 


59 


resulted  in  the  removal  of  a  quantity  of 
heat,  Qi,  from  the  hot  body,  the  doing 
of  a  certain  amount  of  external  work,  E, 
and  the  rejection  to  the  cold  body  of  a 
certain  amount  of  heat,  Q2>  equal  to  Qi  —E. 
When  reversed  the  same  amount  of  heat, 
Q2,  would  be  absorbed  from  the  cold  body, 
the  same  *  amount  of  work,  E}  would  be 
received  from  outside  sources,  and  the  sum 
of  the  two,  Q,  would  be  given  to  the  hot 
body.  In  this  form  the  apparatus  may 
be  considered  a  heat-pump,  since  it  car- 
ries heat  from  a  lower  to  a  higher  tem- 
perature. 

The  full  extent  of  the  meaning  of  the 
term  "reversible"  should  be  understood. 
In  the  sense  in  which  the  word  is  used 
here,  no  process  is  reversible  unless  at  its 
completion  it  can  be  immediately  carried 
through  in  the  opposite  direction  with  no 
change  of  apparatus.  Thus  in  the  Carnot 
method  of  applying  heat  along  an  isother- 
mal or  at  constant  temperature,  the 
process  is  reversible  because  the  heat 
could  again  be  rejected  with  all  changes 


60 


exactly  opposite  to  those  during  reception 
by  a  simple  reversal  of  the  direction  of 
motion  of  the  piston.  As  an  example 
of  a  non-reversible  process,  imagine  the 
heating  of  a  gas  by  bringing  it  into  con- 
tact with  a  body  at  a  higher  temperature. 
No  method  of  doing  this  can  be  imagined 
by  a  reversal  of  which  the  heat  can  be 
again  extracted  from  the  gas  and  given 
back  to  the  source  of  supply  while  that 
gas  is  in  contact  with  the  high-temperature 
body;  that  is,  no  method  which  will  result 
in  leaving  the  body  at  the  initial  high 
temperature  and  the  gas  at  the  initial 
low  temperature,  and  which  will  not  in- 
volve the  use  of  additional  apparatus. 
An  example  of  a  non-reversible  process 
in  actual  practice  is  the  heating  of  the 
working  fluid  in  an  internal-combustion 
engine  by  the  chemical  process  of  com- 
bustion. 

An  engine,  then,  which  is  reversible  in 
this  thermodynamic  way,  when  run  as  a 
pump  absorbs  the  same  amount  of  work 
as  it  previously  made  available,  takes 


61 


from  the  cold  body  the  same  amount  as 
it  previously  rejected  to  it,  and  gives  to 
the  hot  body  the  same  amount  as  it  pre- 
viously absorbed  from  it.  It  is  a  simple 
matter  to  prove  that  such  a  reversible 
engine  has  the  maximum  possible  theo- 
retical efficiency. 

For  this  purpose  imagine  a  reversible 
engine  and  another  engine  of  any  kind 
which  is  assumed  to  be  capable  of  de- 
veloping exactly  the  same  amount  of 
useful  or  external  work,  but  is  more 
efficient,  that  is,  absorbs  less  heat  from 
the  hot  body  for  the  purpose  of  de- 
veloping that  work.  Since  both  en- 
gines are  equally  powerful,  either  one  can 
drive  the  other,  and  it  may  therefore  be 
assumed  that  the  more  efficient  may  be 
made  to  drive  the  reversible  engine  as  a 
heat-pump,  removing  an  amount  of  heat, 
Q2,  from  the  cold  body  and  giving  an 
amount  of  heat,  Qi,  to  the  hot  body. 
But  since  the  driving  engine  which  is 
developing  the  external  work  which  the 
pump  is  absorbing  is  more  efficient  than 


62 


the  pump,  it  is  removing  from  the  hot 
body  an  amount  of  heat,  Q\,  less  than  Qi> 
and  rejecting  to  the  cold  body  an  amount 
of  heat,  Q2',  less  than  Q2. 

The  result  of  assuming  the  driving' 
engine  more  efficient  than  the  driven  is 
to  develop  a  system  which,  without  the 
reception  of  any  energy  from  outside 
sources,  is  capable  of  conveying  more 
heat  from  a  low  to  a  high  temperature 
than  it  carries  from  the  high  to  the  low 
temperature  in  keeping  itself  in  operation. 
This  action  is  contrary  to  common  ex- 
perience as  expressed  in  the  Second  Law 
of  Thermodynamics,  and  is  regarded  as 
an  absurdity.  Therefore  the  driving  en- 
gine cannot  have  an  efficiency  greater  than 
that  of  the  reversible  engine;  the  best 
that  it  can  do  is  to  have  an  equal  efficiency. 
Since  the  driving  engine  was  not  specified 
as  to  type,  the  proof  is  absolutely  general, 
depends  only  on  common  experience  as 
stated  in  the  Second  Law,  and  shows 
the  reversible  engine  to  have  as  high  an 
efficiency  as  is  attainable. 


63 


It  is  only  one  step  farther  to  show  that 
all  engines,  reversible  in  the  same  way 
as  the  Carnot  engine  is  reversible,  must 
have  the  same  efficiency  when  operating 
between  the  same  temperature  limits  no 
matter  what  their  cycle  of  operations. 
If  this  were  not  so,  the  more  efficient 
could  be.  made  to  drive  the  less  efficient, 
giving  the  absurdity  described  above. 

/rr    rp 

The  Carnot  efficiency  —^= — -   is    then 

^i 

the  maximum  possible  theoretical  effi- 
ciency which  may  be  obtained  with  heat- 
engines.  For  this  reason  it  is  often  used 
as  a  standard  with  which  to  compare  the 
performances  of  actual  engines. 


CARNOT  CYCLE    ON    T(j>   DIAGRAM. 

The  shape  of  the  Carnot  cycle  when 
drawn  on  the  T(f>  diagram  must  be  as 
shown  in  Fig.  6,  because  the  lines  ab 
and  cd  are  lines  of  constant  temperature, 
and  the  lines  be  and  ad  are  adiabatics, 
that  is,  lines  of  constant  entropy. 


64 

Equation    (51),  which   applies   to   this 
case,  gives 

Q-T^fa-fa)     and    Q2  =  W2-0i), 
so  that  the  efficiency  becomes 

Qi  -Q2_^i  (<fe-<£i)-  T2(<f>2  -fa) 


™  = 


l~2  as  before.        (59) 
-*  i 


Since  the  area  under  ab  represents  heat 
received  from  the  hot  body  and  the 
area  under  cd  represents  heat  rejected 
to  the  cold  body,  the  area  abed,  which  is  the 
difference  between  them,  must  equal  the 
heat  converted  into  external  work. 

It  can  readily  be  seen  from  the  diagram 
of  Fig.  6  and  the  following  demonstration 
that  the  criterion  of  maximum  efficiency 
is  the  reception  at  the  highest  tempera- 
ture of  all  the  heat  received  from  the  hot 
body  and  the  rejection  at  lowest  tempera- 
ture of  all  heat  rejected  to  the  cold  body. 
If  the  heat  is  received  at  temperatures 
varying  between  TJ  and  7\,  the  line 


65 


showing  entropy  change  will  be  given  by 
equation  (53)  and  will  have  a  shape  ap- 
proximately that  shown  by  dotted  line 
d'a'  of  Fig.  6.  This  would  result  in  the 


I-'IG 


loss  of  area  d'aa' ',  which  is  a  much  larger 
proportion  of  area  abed  than  it  is  of  area 
abef,  and  therefore  the  efficiency,  which" 
win  now  be 


Eff.= 


a'bcdd' 
a'befd' 


66 


will  be  less  than  the  previous  efficiency, 
which  was 

™     abed 

Mt.  =  — r— -, 

abef 

and  a  similar  proof  holds  for  rejection 
of  heat  at  any  temperature  other  than 
7\  as  along  the  line  b'c'. 

STIRLING   CYCLE. 

There  is  an  apparent  exception  to  the 
above  criterion  of  maximum  efficiency 
in  the  case  of  certain  cycles  which  have 
been  proposed  and  of  which  the  so-called 
u  Stirling  "  cycle  is  an  example. 

In  this  cycle,  which  is  graphically 
compared  with  a  Carnot  cycle  for  same 
temperature  range  in  Fig.  7,  the  working 
substance  is  expanded  isothermally  with 
reception  of  heat  from  the  body  at  tem- 
perature Tij  until  reaching  point  b, 
when  some  of  its  heat  is  transferred  to  a 
device  known  as  a  regenerator.  The 
apparatus  is  so  arranged  that  the  pressure 
drops  with  the  temperature  at  just  the  rate 
necessary  to  keep  the  volume  constant. 


67 


\ 


\ 


\ 


c' 


FIG.  r. 


68 


The  regenerator  is  a  device  which  can 
receive,  store,  and  restore  heat.  For 
purposes  of  illustration  it  may  be  assumed 
to  be  a  long  pipe,  with  temperature 
graded  from  T\  to  T2.  through  which  the 
material  can  flow,  giving  up  heat  at  just 
such  a  rate  as  to  keep  its  volume  constant 
while  its  pressure  decreases,  arriving  at 
the  temperature  T2  when  its  pressure  has 
dropped  to  that  shown  at  point  c'. 

Then  the  material  is  compressed  in 
contact  with  a  cold  body,  giving  an  iso- 
thermal compression  at  temperature  T2 
untjl  the  point  dr  is  reached.  The  mate- 
rial is  then  passed  through  the  regenerator 
in  the  reverse  direction,  taking  up  the 
heat  which  it  previously  rejected,  until 
arriying  at  the  pressure  shown  at  a  with 
the  !  corresponding  temperature  TI  . 

Tjhe  efficiency  of  such  a  cycle  would  be 


Heat  Supplied  from  hot  body 
RTl\ogcr-RT2\o&r  _  Tl-T2 
RTl  log,r  Tl     ' 


69 


which  is  seen  to  be  the  same  as  the  Carnot 
cycle.  This  does  not  contradict  the 
criterion  of  maximum  efficiency  previously 
arrived  at,  because,  although  the  body 
receives  heat  at  varying  temperatures 
along  the  line  d'a  and  rejects  it  similarly 
along  the  line  be',  all  ihe  heat  received  into 
the  system  from  the  hot  body  is  received 
at  the  highest  temperature,  and  all  that 
rejected  from  the  system  to  the  cold 
body  is  rejected  at  the  lower  temperature. 
The  T(j>  diagram  for  such  a  cycle  is 
shown  in  Fig.  8,  where  it  is  the  figure 
abc'd'  superimposed  upon  the  Carnot 
cycle  abed.  The  lines  d'a  and  c'b  are 
obtained  by  means  of  equation  (55)  and 
are  readily  seen  to  be  parallel  curves,  so 
that  the  areas  d'ad  and  c'bc  are  equal  and 
therefore  the  areas  abc'd'  and  abed  are 
equal.  The  efficiency  in  each  case  is  the 
area  of  the  cycle  divided  by  the  area 
abef,  which  is  the  heat  received  along  the 
line  ab,  and  therefore  the  two  efficiencies 
are  equal.  The  heat  received  by  the  hot 
body  along  d'a  and  rejected  along  the 


70 


line  be'  never  really  leaves  the  system  or 
apparatus  and  may  be  considered  as 
simply  short-circuited  during  part  of  the 
cycle. 


FIG.  8. 


OTTO   CYCLE. 

Another  cycle  of  interest  is  the  "  Otto  " 
cycle,  which  is  the  theoretical  cycle  of 
most  of  the  gas-engines  built  at  the  present 
time.  Drawn  on  the  PV  diagram,  it  has 
the  shape  shown  in  Fig.  9.  Heat  is  added 


71 


to  the  gas  at  conditions  shown  at  point  a, 
causing  a  rise  of  pressure  to  P*  while  the 
volume  is  maintained  constant.  Then 
adiabatic  expansion  takes  place  with  a 
fall  of  temperature  and  pressure  until  the 
volume  equals  that  shown  at  c,  where  heat 
is  rejected  at  const-ant  volume  until  the 
pressure  has  fallen  to  P*,  where  adiabatic 
compression  is  used  to  bring  the  material 
back  to  initial  pressure  and  volume. 

In  actual  practice  the  working  substance 
is  changed  at  even-  cycle,  a  charge  erf  mixed 
air  and  combustible  being  drawn  into  the 
cylinder  along  the  line  <f«f,  then  carried 
through  the  cycles  as  shown,  heat  being 
supplied  along  ab  by  the  sudden  com- 
bustion or  explosion  of  the  compressed 
mixture.  When  point  c  is  reached  the 
exhaust-valve  is  opened  and  the  pressure 
suddenly  drops  while  some  of  the  burned 
gas  blows  out  into  the  atmosphere,  which 
in  this  case  acts  as  the  cold  body  or  con- 
denser. The  remainder  of  the  products 
of  combustion  is  exhausted  along  the 
fine  dtf  .  Thus  while  in  the  theoretical 


73 


case  the  working  substance  is  the  same 
time  after  time,  and  two  strokes  are  neces- 
sary for  each  cycle,  in  the  actual  case  the 
working  substance  is  changed  each  cycle 


a' 


FIG.  10. 

and  it  requires  four  strokes  to  complete 
a  cycle. 

Fig.  10  shows  the  shape  of  this  cycle 
on  the  T(j>  diagram.  The  letters  of  Figs. 
9  and  10  designate  corresponding  points. 

The  line  ab  in  the  T<j>  diagram  repre- 
sents the  addition  of  heat  *4  constant 


74 


volume,  and    the    change    of   entropy   is 
given  by 


the  heat  added  is 


Adiabatic  expansion  with  <£  constant 
is  given  by  the  line  be.  The  rejection  of 
heat  to  the  cold  body  while  volume  re- 
mains constant  is  given  by  cd  with  entropy 
change  : 

T 

(f>=Cv\ogel~, 

and  the  heat  rejected  is 


Writing  efficiency  as 

M-^4p 

Eff.=»-/<r" 


C,(Tb-Ta) 

(61) 


f  6~^  o 


75 


Since  the  curves  be  and  da  represent 
adiabatic  changes,  the  ratio  of  the  various 
temperatures  may  be  expressed  by  means 
of  equation  (44)  as 


Tb     \V< 

and 

T*      /V  \r-i 
_=  / _  a  » 

and  therefore 

•^r  =  ^r-     and 


rri          rji  i.         ™  ™  „    . 

*  b      *  a  *  b —  ^  a       ^  o 

Equation  (61)  may  then  be  written 

Eff.  =  l-p  =  ^d,  (62) 

la  la 

or 

Eff^l-^-1;  (63) 

showing  the  rather  curious  fact  that  the 
efficiency  of  this  cycle  theoretically  de- 
pends only  upon  the  temperature  ratio 
or  volume  ratio  of  the  adiabatic  com- 
pression. 


76 


This  cycle  can  be  graphically  compared 
with  the  Carnot  cycle  for  same  tempera- 
ture limits  by  means  of  the  diagram 
a'bc'd,  and  the  efficiency  for  the  Otto  cycle 
can  be  shown  to  be  less  than  that  of  the 
Carnot  by  a  discussion  similar  to  that 
given  for  the  dotted-line  cycle  of  Fig.  6. 

REFRIGERATING-MACHINES. 

Refrigerating-machines  using  gases  for 
a  working  substance  are  still  used  to  a 
certain  extent,  and  therefore  their  cycles 
should  be  considered  here.  In  the  dis- 
cussion of  the  Carnot  engine  it  was  shown 
that  when  reversed  it  acted  as  a  heat- 
pump,  removing  heat  from  the  bqdy  at  a 
low  temperature  and  rejecting  it  to  a 
body  at  a  high  temperature.  Thus  a 
heat-pump  is  nothing  but  what  is  ordi- 
narily known  as  a  refrigerating-machine. 

Any  reversible  cycle  could  be  used  for 
refrigerating-machinery,  though  all  re- 
versible gas-cycles  are  very  inconvenient 
for  practical  application.  Several  cycles 


77 


which  are  not  thermodynamically  re- 
versible may  in  a  different  sense  be  car- 
ried through  in  the  reverse  direction  by 
properly  constructed  mechanism.  That 
is,  apparatus  can  be  devised  which  when 
operated  gives  a  cycle  traced  in  the  counter- 
clockwise direction  similar  to  that  traced 
in  a  clockwise  direction  by  an  engine. 

THE   JOULE   CYCLE. 

The  Joule  cycle  is  a  very  good  example 
of  such  conditions.  It  has  the  shape 
shown  in  Fig.  11,  when  drawn  to  PV 
coordinates.  The  operation  when  the 
cycle  is  traced  by  an  engine  is  as  follows: 
Gas  with  pressure  and  volume  as  shown 
at  a  is  compressed  adiabatically  to  con- 
ditions at  b '['  "it  is  then  brought  in  contact 
with  a  hot  body  at  temperature  equal  to 
jfi,  greater  than  that  of  the  gas  at  b. 
Heat  is  received,  and  pressure  maintained 
constant  while  temperature  and  volume 
increase  until  conditions  are  as  shown 
at  c.  The  temperature  of  the  gas,  T 'c, 


78 


79 


may  or  may  not  be  as  great  as  TI;  it 
cannot  be  greater.  Adiabatic  expansion 
brings  the  body  to  conditions  Vd  and  Pa, 
and  then  the  heat  is  rejected  to  a  body 
at  low  temperature,  T^  while  the  volume 
and  temperature  decrease  with  constant 
pressure.  The  temperature  T%  must  be 
at  least  as  low  as  Ta,  and  may  be 
lower. 

To  make  this  device  act  as  a  heat-pump 
the  gas  must  expand  at  constant  pressure 
from  V a  to  Vd,  while  the  temperature 
rises,  due  to  the  absorption  of  heat  from 
the  cold  body.  That  body  must  now 
have  a  temperature  at  least  as  high  as  Ta, 
showing  immediately  that  this  cycle  is  not 
thermodynamically  reversible,  because  a 
change  of  apparatus  is  necessary  for  re- 
versal. The  line  from  d  to  c  represents 
adiabatic  compression,  and  at  c  the  gas 
begins  to  reject  heat  to  the  hot  body, 
which  now  must  have  a  temperature  no 
higher  than  that  of  the  gas  when  at  F&P&. 
The  rejection  of  heat  continues  until  point 
b  is  reached,  when  the  gas  is  expanded 


so 


adiabatically  to  a  and  the  cycle  is  com- 
plete. 

The  performance  of  the  cycle  has  re- 
sulted in  removing  an  amount  of  heat,  Q2, 
from  the  cold  body,  and  the  giving  to  the 
hot  body  of  an  amount,  Qi>  equal  to  Q% 
plus  the  work  of  compression  from  d  to  c. 

The  cycle  as  drawn  to  T<p  coordinates 
is  shown  in  Fig.  12  where  all  the  letters 
correspond  to  those  in  Fig.  11.  The  heat 
removed  from  the  cold  body  is  given  by 
the  area  eadf,  which  represents  the  amount 
of  heat  received  by  the  gas  at  constant 
pressure  and  is  equal  to 

Q2  =  Cp(Td-Ta). 

The  heat  added  to  the  hot  body  is  simi- 
larly the  area  ebcf,  and  equals 

Qi  =  Cp(Te-Tb). 

The  useful  result  in  this  cycle  is  the 
amount  of  heat  removed  from  the  cold 
body,  and  the  expenditure  of  energy  is 
the  amount  received  from  external  sources 


81 


©       o* 


Q 

— 

to 


82 


to  drive  the  machine,  that  is,  Qi— Q2. 
Therefore  the  efficiency  should  be 


TTff  _       ^2       _  Cp(Td  —  Ta) 


z    CP(Tc-Tk)-CP(Td-Ta) 

Td-Ta 


(64) 


(Tc-Tb) -(Td-Ta) 
Writing  the  reciprocal  of  this  equation, 

1    =Qi-Q2=(Tc-Tb)-(Td-Ta) 
Eff.        Q2  Td-Ta 

=  Td-Ta~1' 

but  from  equation  (46) 

\f-i 


so  that  since  Pb  =  Pc  and  Pa  =  Pd, 


Ta       Td       Td-Ta       \Pa 

which  substituted  above  gives 

JL  -Tb   i=Tb-Ta 

Eff.'       Ta  Ta      ' 


83 

or 

r-i        r-i 
il          PbY   -P   ? 
r  ~1  = ET~~' 

Pa7 

giving 

r-i 

Eff.  =  ^-^-=     ^r    r_i?  .     (65) 

a  result  which  it  can  be  seen  depends 
only  on  the  temperature  or  pressure 
ratio  of  the  expansion  ab,  and  may  have 
any  value  less  than  or  greater  than  unity. 
It  is  interesting  to  note  that,  unlike  the 
heat  engine  cycle,  the  efficiency  of  this 
refrigerator  cycle  is  the  greatest  when 
temperature  range  is  smallest  and  its 
thermodynamic  efficiency  may  be  greater 
than  unity. 


CHAPTER  V. 
FLOW  OF  GASES. 

THE  flow  of  gases  through  pipes  and 
nozzles  may  be  investigated  by  means 
of  thermodynamic  equations  slightly  modi- 
fied to  fit  the  conditions.  The  equations 
derived  vary  somewhat  as  the  assumed 
conditions  of  flow  vary,  and  as  the  limits 
of  this  small  book  preclude  a  lengthy 
discussion,  only  the  simplest  case  will  be 
considered. 

Assume  a  very  large  reservoir  which  is 
constantly  supplied  with  gas  at  a  pressure 
PI  so  that  the  pressure  within  the  vessel 
is  always  maintained  -at  that  value.  The 
corresponding  temperature  is  TI,  and  the 
volume  of  unit  weight  is  V\.  Further, 
assume  a  short  pipe  connected  into  the 
side  of  the  vessel,  as  shown  in  Fig.  13, 
84 


85 


in  such  a  way  as  to  give  rounded  corners 
at  a,  so  that  the  gas  may  enter  it  without 
serious  disturbance.  If  this  short  pipe 
or  nozzle  communicate  with  a  large  space 


FIG.  13. 

in  which  a  constant  lower  pressure,  PS,  is 
maintained,  there  will  be  a  steady  flow 
of  gas  as  indicated  by  the  arrow.  In 
order  that  this  steady  flow  through  the 
nozzle  may  be  maintained,  the  gas  within 
the  reservoir  at  some  distance  from  that 


86 


opening  will  have  to  flow  toward  it  with 
a  constant  and  definite  velocity,  which 
may  be  designated  as  v\.  Within  the 
tube  the  gas  will  have  some  pressure^ 
P2,  lower  than  Px  and  higher  than  P3, 
and  some  velocity,  v2,  greater  than  v\. 

If  the  gas  be  assumed  to  receive  no  heat 
from,  and  to  give  no  heat  to,  external 
sources  during  its  flow,  the  total  energy 
associated  with  one  pound  of  material 
in  the  nozzle  at  pressure  P%  must  equal 
the  total  energy  associated  with  that 
same,  or  a  similar,  pound  when  in  the 
reservoir  under  pressure  PI.  Equating 
these  two  quantities  gives  a  very  con- 
venient fundamental  equation.  « 

Every  pound  which  leaves  the  reservoir 
under  the  pressure  PI  must  be  forced  out 
of  that  reservoir,  and  therefore  external 
work  equal  to  P\V\  must  be  done  upon 
it  just  as  though  it  were  being  forced  out 
by  a  piston  which  swept  through  the 
volume  Vi  under  the  pressure  PI  in  dis- 
charging one  pound  of  gas. 

Similarly,  every  pound   of  gas  flowing 


87 


in  the  nozzle  under  pressure  P2  displaces 
its  own  volume  against  the  constant  pres- 
sure P<2  and  does  an  amount  of  work  P2V2, 
just  as  if  it  drove  a  piston  through  the 
volume  ¥2  under  the  constant  pressure 

P2. 

Every  pound  has  a  certain  amount  of 
kinetic  energy  when  in  the  large  reservoir, 
due  to  its  velocity  vi,  and  a  certain  differ- 
ent amount  of  kinetic  energy  when  in  the 
small  tube  and  moving  with  velocity  v2. 

Further,  every  pound  in  the  reservoir 
has  a  certain  amount  of  energy  associated 
with  it  in  the  form  of  sensible  heat,  and 
the  same  is  true  of  every  pound  as  it  flows 
through  the  tube. 

Equating  total  energy  associated  with 
one  pound  in  the  reservoir  to  total  energy 
associated  with  one  pound  in  the  tube 
gives 

+  JS2,   (66) 


so  that 

1-S2).  (67) 


88 


Since  the  difference  in  sensible  heat  is 
equal  to  the  real  specific  heat  into  the 
difference  of  temperatures, 


and 


The  velocity  in  the  reservoir  may  be 
neglected  as  very  small,  so  that 


Substituting  from  the  law  of  perfect 
gases  and  then  factoring  gives 


PV 
'    ' 


and  since 

R 


89 

it  follows  that 


and 

The  weight  in  pounds  per  second,  W, 
can  be  found  if  the  sectional  area,  a,  of 
the  tube  is  known.  Since 


the  discharge  per  second  is 


With  the  assumption,  made  above,  of  no 
heat-energy  transfer  to  or  from  external 
sources  during  the  flow,  the  drop  in 
pressure  from  PI  to  P%  must  be  an  adia- 
batic  expansion,  and 


90 

so  that 

P2v2=plVl 

and 


Substituting  for  P2V2  in  (68)  gives 


P^^jl-^T-1  j,  (69) 
and  then 


Since 


it  follows  that 


(70) 

These  equations  give  the  velocity  of 
flow  and  the  quantity  discharged  when 


91 


the  initial  conditions  and  the  tube  pressure, 
P2,  are  known.  In  most  problems  of  this 
character  P3,  the  second  reservoir  pressure, 
is  known,  but  P2  is  unknown  and  must  be 
calculated.  Unfortunately  P2  bears  no 
simple  relation  to  P3,  and  the  ratio  be- 
tween the  two  must  be  experimentally 
determined. 

Experiments  with  air  show  that  P2 
decreases  according  to  a  rather  compli- 
cated expression  as  P3  decreases,  until  P3 

p 
has  arrived  at  a  value  equal  to  ~,  when 

2i 

the  value  of  P2  is  approximately  equal  to 
0.58Pi.  Further  decrease  in  the  value 
of  P3  causes  no  diminution  in  the  dis- 
charge-tube pressure.  Thus  the  maxi- 
mum discharge  will  take  place  when  P3 

p 
is  equal  to  or  less  than  -£. 

It  is  interesting  to  note  that  a  mathe- 
matical determination  of  the  pressure  P2 
for  maximum  discharge  can  be  found  by 
means  of  equation  (70),  and  shows  that 
maximum  to  occur  when  P2  is  approxi- 


92 


mately  equal  to  0.53Pi.  Thus  the  theo- 
retical and  experimental  values  apparently 
do  not  check,  but  as  yet  the  experimental 
data  are  rather  meagre,  so  that  the  figure 
given  may  not  be  final.  It  should  also  be 
remembered  that  the  equations  for  flow 
are  determined  for  ideal  conditions  and 
for  perfect  gases,  while  experiments  must 
be  made  with  actual  apparatus  and  with 
real  imperfect  gases. 


CHAPTER  VI. 
VAPORS. 

IN  tfie  chapter  on  gases  it  was  noted 
that  the  laws  developed  for  the  ideal 
"Perfect  Gas"  are  very  approximately 
true  for  the  real  gases  when  far  removed 
from  their  points  of  liquefaction.  The 
nearer  real  gases  are  brought  to  the  tem- 
peratures and  pressures  at  which  lique- 
faction occurs,  the  farther  do  they  deviate 
from  these  laws.  Substances  are  called 
vapors  when  between  the  conditions  under 
which  they  may  be  treated  as  perfect 
gases  and  those  under  which  they  exist 
as  liquids. 

TEMPERATURE   OF  VAPORIZATION. 

Obviously  there  is  no  fixed  point   at 
which  a  substance  ceases  to  be  a  vapor 
93 


and  becomes  a  practically  perfect  gas, 
the  allowable  amount  of  variation  from 
perfect  gas  laws  being  simply  a  matter  of 
personal  taste  or  convenience.  There  is, 
however,  under,  any  given  conditions,  a 
very  definite  and  fixed  point  at  which  a 
liquid  changes  to  a  vapor  or  a  vapor  be- 
comes a  liquid. '  For  e  ery  pressure  there  is 
a  temperature  for  every  substance  above 
which  that  substance  cannot  exist  in  the 
liquid  form.  Each  of  these  tenperatures 
is  called  the  temperature  of  vaporization  for 
the  liquid  under  considerction  for  each  par- 
ticular pressure.  Thus  the  temperature  of 
vaporization  for  water  under  a  pressure 
of  14.7  Ibs.  per  square  inch  is  212° 
Fah  enheit. 

The  temperature  of  vaporization  rises 
with  the  pressure  according  to  laws  which 
must  be  experimentally  determined  for 
every  individual  substance.  This  fact  is 
what  would  naturally  be  expected,  because 
vaporization  is  always  accompanied  by 
an  increase  of  volume,  and  anything  which 
would  tend  to  prevent  this  increase  would 


95 


make  necessary  a  higher  temperature  for 
the  separation  of  the  molecules.  An  in- 
crease of  pressure  might  be  regarded  as 
assisting  the  internal  attractions  in  pre- 
serving the  liquid  form  against  the  sepa- 
rating and  expanding  tendencies  accom- 
panying the  rise  of  temperature  of,  or  the 
increase  of  heat  energy  associated  with, 
the  substance. 

SATURATED  AND  SUPERHEATED  VAPOR. 

A  vapor  which  is  just  on  the  point  of 
liquefaction,  so  that  any  increase  of  pressure 
or  drop  of  temperature  will  cause  partial 
or  total  condensation,  is  called  a  saturated 
vapor.  If  it  be  removed  farther  from  the 
liquid  state  by  even  an  infin'tesimally 
small  amount,  it  is  called  a  "  Superheated 
Vapor. "  Continuing  in  the  same  direc- 
tion, the  material  becomes  finally  a  prac- 
tically perfect  gas.  It  is  therefore  possi- 
ble to  regard  a  perfect  gas  simply  as  a 
very  highly  superheated  vapor,  and  to 
take  the  extent  of  superheating  as  a 
measure  of  gaseous  perfection. 


96 


PROCESS   OF  VAPORIZATION. 

The  laws  of  vapors  are  most  easily 
developed  by  studying  the  production  of 
vapor  from  a  liquid,  and  then  the  gradual 
development  of  a  more  and  more  nearly 
perfect  gas  from  that  vapor  as  it  is  super- 
heated. 

Assume  for  this  purpose  a  non-conduct- 
ing cylinder  with  axis  vertical  and  fitted 
with  a  frictionless  piston.  Beneath  this 
piston  imagine  unit  weight  of  a  liquid  and 
assume  the  piston  to  have  such  weight  as 
to  exert  a  pressure  of  P  pounds  per  square 
foot  on  the  surface  of  the  liquid. 

If  now  the  liquid  be  heated,  it  will 
rise  in  temperature  with  a  slight  increase 
of  volume,  absorbing  heat  equal  to 

Q  =  C(T2-T1),  (71) 

where  T2  and  T\  are  final  and  initial  tem- 
peratures, and  C  is  the  average  specific 
heat  for  that  temperature  range. 
The  temperature  will  continue  to  rise 


97 


until  a  value  is  reached  at  which,  under 
the  existing  pressure,  vaporization  will 
take  place.  Further  addition  of  heat 
will  then  cause  vaporization  with  an 
enormous  increase  of  volume  but  no  in- 
crease of  temperature  until  all  of  the 
liquid  has  been  evaporated.  If  heat  be 
added  after  the  vaporization  is  complete, 
the  volume  will  still  further  increase 
and  the  temperature  will  rise  until  the 
material  is  finally  so  far  removed  from 
the  liquid  state  as  to  be  a  sensibly  perfect 
gas. 

If  the  operation  is  repeated  with  a  piston 
of  different  weight,  the  same  series  of 
events  will  take  place,  but  the  values 
of  temperature,  volume,  and  heat  supplied 
will  be  different.  A  piston  giving  a  greater 
pressure  per  square  foot  will  cause  a  higher 
temperature  of  vaporization,  a  smaller 
volume  of  resultant  saturated  vapor,  and 
the  absorption  of  a  different  quantity  of 
heat  during  vaporization.  A  piston  giving 
a  pressure  less  than  the  first  will  cause 
a  lower  temperature  of  vaporization,  a 


larger  saturated  vapor  volume,  and  a  still 
different  heat  absorption. 

HEAT   CONTENT  OF  VAPOR. 

It  is  convenient  to  consider  the  heat 
required  for  the  process  of  vaporization  as 
divided  into  three  parts: 

(1)  Heat  necessary  to  raise  the  tem- 
perature of  liquid  to  the  temperature  of 
vaporization,  which  heat  is  called  ''Heat 
of    the   Liquid"    and    represented   by    q 
when  dealing  with  unit  weight  of  material. 

(2)  That  necessary  to  change  the  liquid 
at  vaporization  temperature   to  a  satu- 
rated  vapor   at   the   same   temperature, 
known  as  "Latent  Heat  of  Vaporization" 
and  represented  by  r  when  dealing  with 
unit  weight. 

(3)  Heat    necessary    to    superheat    or 
raise  the  temperature  of  the  vapor  above 
the  temperature  of  saturation,  known  as 
" Superheat"  and  generally   expressed  in 
terms  of  the  temperature  to  which  super- 
heating has  been  carried;  that  is,  a  vapor 


99 


is  spoken  of  as  having  a  certain  number 
of  degrees  of  superheat,  meaning  that  it 
has  been  raised  that  many  above  the 
temperature  of  vaporization.  The  de- 
gree of  superheat  is  most  often  represented 
by  D. 

The  latent  heat  of  vaporization,  r,  is 
still  further  divided  into  two  parts: 

(a)  The  Internal  Latent  Heat  of  Vapori- 
zation, designated  by  p  for  unit  weight. 

(6)  The  External  Latent  Heat  of  Vapori- 
zation, designated  by  the  group  symbol 
APu,  when,  as  before,  dealing  with  unit 
weight. 

The  first,  (a),  represents  the  heat  neces- 
sary to  do  the  internal  work  of  separation 
of  molecules  when  the  volume  changes 
from  that  of  a  liquid  to  that  of  a  saturated 
vapor.  The  second,  (6),  represents  the 
heat  necessary  to  do  the  work  of  dis- 
placing the  surrounding  or  enveloping 
medium,  as  the  driving  out  of  the  piston 
in  the  case  just  considered. 

The  group  of  symbols,  APu,  is  equiva- 
lent to  the  expression  already  developed 


100 

"  for  external  work  during  constant  pres- 
sure expansion,  that  is,  P(V2  —  FI).  Since 
this  expression  is  in  "terms  of  pounds  and 
feet,  the  result  will  be  foot-pounds  of 
work.  To  express  the  same  quantity  in 
British  Thermal  Units  (B.T.U.)  it  must 
be  divided  by  Joule's  Equivalent,  J=778. 

Representing  j  by  A,  and  (V2  —  Vi)  by 

u,   the  expression  for  external  work  in 
British  Thermal  Units  becomes 


which  is  the  form  used  in  dealing  with 
liquids  and  vapors. 

To  sum  up,  the  quantity  of  heat  per 
unit  of  weight  which  must  be  added  to  a 
liquid  to  convert  it  into  a  more  or  less 
perfect  gas  at  a  temperature  above  that 
of  vaporization  is 

Q  =  Heat  of  liquid  +  Heat  of  vaporization 
+  Superheat, 

which  may  be  represented  in  symbols  by 
putting 


101 


of 

where  T\    is   initial   temperature 
of   liquid   and    Tv    is    vaporizing 
temperature    under    the   existing 
pressure  conditions; 
r=heat  of  vaporization  =  p  +  APu, 

and 

CVD  =CV(T8  -  TV)  =  Superheat, 

where  C  is  the  specific  heat  of  the 
vapor  and  D  represents  the  num- 
ber of  degrees  to  which  the  sub- 
stance is  raised  above  vaporization 
temperature, 

giving 

(72) 


If  the  liquid  is  converted  into  saturated 
vapor  but  not  superheated,  a  case  occur- 
ring so  frequently  that  the  special  symbol 
A  is  used  to  represent  the  heat  required, 

Q  =  q  +  r=l  =  q  +  p  +  APu  =  S  +  I  +  E.   (73) 

If  the  liquid  is  only  partly  vaporized, 
that  is,  all  raised  to  the  temperature  of 


102 

vaporization  and  then  oniy  enough  heat 
added  to  convert  x/100  of  it  to  the  vapor- 
ous form,  the  expression  for  heat  per 
pound  takes  the  form 


The  term  x  is  called  the  "  quality"  and 
is  generally  given  in  per  cent.  Thus  a 
quality  of  75%  means  a  mixture  of 
0.75  by  weight  of  saturated  vapor  and  0.25 
liquid  at  the  temperature  of  vaporization. 
As  a  matter  of  custom,  the  letter  x  is 
used  indifferently  to  represent  per  cent 
quality  and  the  fraction  x/100  as  given 
above,  so  that  equation  (73)  is  generally 
written 

Q=q  +  xr.  (75) 

This  expression  will  of  course  give  the 
correct  value  independent  of  the  state  of 
mixture  of  liquid  and  vapor,  that  is,  it 
makes  no  difference  whether  the  liquid  is 
all  collected  at  the  bottom  of  a  vessel 
with  the  vapor  above  it,  or  the  liquid  in 
the  form  of  small  drops  is  distributed 


103 

throughout  the  entire  volume  of  the 
vapor.  The  latter  is  the  condition  more 
often  met  with  in  practice. 

A  mixture  of  a  saturated  vapor  with 
its  liquid  is  spoken  of  as  a  Wet  Vapor, 
and  a  saturated  vapor  existing  absolutely 
free  of  its  liquid  is  called  a  Dry  Vapor. 
Thus  starting  with  liquid,  the  complete 
list  of  the  various  possible  forms  is 

(a)  Liquid  below  temperature  of  vapori- 
zation. 

(6)  Liquid  at  temperature  of  vaporiza- 
tion. 

(c)  Mixture  of  liquid  and  vapor,  or  wet 
saturated  vapor. 

(d)  Dry  saturated  vapor. 

(e)  Superheated  vapor. 

(/)  Very  highly  superheated  vapor,  or 
practically  perfect  gas. 

Studying  the  heat  content  of  vapors  in 
accordance  with  equation  (2), 


the  quantity   q  may  be  taken    as    the 
sensible  heat  S  if  the  small  increase  of 


104 

volume  of  liquid  with  temperature  rise 
be  neglected;  the  quantity  p  may  repre- 
sent the  heat  of  internal  work,  7;  the 
quantity  APu  the  heat  of  external  work. 
Thus  q  +  p  might  be  called  the  intrinsic 
energy  of  a  dry  vapor,  and  q  +  xp  the  in- 
trinsic energy  of  a  wet  vapor,  both  above 
32°  F. 

In  the  case  of  a  superheated  vapor 
the  additional  heat  must  be  divided  into 
intrinsic  energy,  or  /S  +  7,  and  energy  of 
external  work,  E.  That  is,  part  is  used 
to  increase  the  temperature  and  to  sepa- 
rate the  molecules  against  their  mutual 
attractions,  and  part  to  displace  the  sur- 
rounding media.  Measuring  the  last, 
the  sum  of  the  first  two  can  be  found  by 
substitution  from  the  total  heat  of  super- 
heat. 

VAPOR   TABLES. 

The  values  of  the  various  quantities 
of  heat  required  for  different  purposes 
during  the  vaporization  processes  of 
various  liquids  are  determined  by  experi- 


105 

ments  assisted,  or  rather  completed,  by 
thermodynamic  calculations.  It  is  there- 
fore convenient  to  arrange  them  in  tables, 
so  that  they  are  readily  obtainable.  Such 
tables  are  known  as  vapor  tables,  or, 
taking  cognizance  of  the  material  to 
which  their  values  apply,  Steam  Tables, 
Ammonia  Tables,  Carbon-dioxide  Tables, 
etc.  In  the  first  two  columns  of  such 
tables  are  generally  given  pressures 
increasing  by  convenient  increments 
through  the  entire  experimental  range, 
and  the  corresponding  temperatures  of 
vaporization,  that  is,  the  temperature  at 
which  vaporization  of  that  particular 
liquid  will  occur  under  each  pressure  tabu- 
lated. Following  these  are  given  in 
separate  columns  each  of  the  quantities 
g,  r,  p,  APu,  ^,  and  then  other  convenient 
data,  such  as  specific  volume,  etc.,  for 
each  pressure  or  temperature. 
Since 


and  only  Tv,  the  temperature  of  vapori- 


106 

nation,  is  fixed  by  the  pressure,  it  is  cus- 
tomary to  assume  the  value  T\  at  some 
convenient  figure  for  each  liquid.  Thus 
it  is  common  to  construct/  steam  tables  to 
give  heat  of  liquid,  q,  and  total  heat,  A, 
above  the  temperature  of  32°  F.,  that  is, 
TI  is  arbitrarily  set  at  32°  F.  For  other 
tables  different  but  equally  convenient 
values  of  TI  are  chosen. 

GRAPHIC    REPRESENTATION    OF    VAPORIZA- 
TION. 

The  entire  process  of  vaporization  and 
superheating  of  water  at  several  pressures 
is  shown  graphically  by  Fig.  14.  The 
specific  heat  of  liquid  water  has  been  con- 
sidered constant  for  this  diagram,  so  that 
ab  is  a  straight  line.  This  line  would  be 
curved  had  the  real  variable  specific  heat 
been  used .  In  studying  the  figure  it  should 
be  noticed  what  a  large  part  of  the  total 
heat  of  the  superheated  vapor  is  that 
absorbed  during  the  process  of  vaporiza- 
tion. 


107 


3 


10 


cq 


*\ 

•Al 


\ 


108 

This  figure  shows  that  while  the  total 
heat  above  32°  F.  per  pound  of  dry  and 
saturated  vapor  increases  as  the  tempera- 
ture increases,  the  latent  heat  of  vapori- 
zation decreases.  The  reason  for  this  is 
that  the  latent  heat  is  made  up  of  two 
quantities,  the  internal  and  external  heats, 
and  that  while  the  external  latent  increases 
the  internal  latent  heat  decreases.  It  is 
easily  seen  that  as  the  temperature  of  a 
liquid  increases  the  bonds  between  the 
molecules  are  constantly  weakening,  so 
that  it  is  reasonable  to  expect  the  heat 
necessary  to  do  the  work  of  separation 
during  vaporization,  that  is,  the  internal 
latent  heat,  to  decrease.  On  the  other 
hand,  as  the  temperature  and  therefore 
the  pressure  rises,  the  volume  of  vapor 
formed  from  a  given  weight  of  liquid  con- 
stantly decreases.  Therefore  the  change 
of  volume  becomes  smaller  as  the  pressure 
becomes  greater.  The  external  latent 
heat  being  obtained  as  the  product  of 
change  of  volume  by  pressure  will  depend 
for  its  value  on  the  relative  rate  of  change. 


109 


Temperature 


01 


"*? 


-o 


/ 


110 

In  the  case  of  water  the  external  latent 
heat,  that  necessary  to  do  this  external 
work,  becomes  greater  as  the  pressure 
rises,  but  increases  less  rapidly  than  the 
internal  latent  heat  decreases.  Their 
sum,  therefore,  must  decrease.  This  con- 
/dition  of  affairs  might  of  course  be  true 
for  water  and  yet  not  for  all  other  vapors, 
and  the  performance  of  each  must  be 
determined  experimentally. 

A  T(j>  diagram  for  this  same  process 
is  very  useful  and  is  given  in  Fig.  15.  As 
in  the  case  of  the  tables  and  the  diagram 
of  Fig.  14,  an  arbitrary  0  is  chosen;  in 
this  case  the  entropy,  (£,  is  figured  above 
32°  F.  Using  equation  (53)  and  assuming 
the  specific  heat  of  liquid  constant, 

02-&  =  <fr  above  32  =-C«  log, 


so  that  the  lines  ab  are  readily  plotted. 
Entropy  above  any  temperature  T\  other 
than  (32+461)  may  of  course  be  found 
by  substituting  that  value  of  T\  for 
(32+461)  in  this  equation. 


Ill 

ENTROPY   OF  VAPOR. 

Since  the  process  of  vaporization  occurs 
at  constant  temperature,  equation  (48) 
may  he  written 

<f>2  —  <f>i  =  <f>v  =  change  of  (j>  during  vapori- 

zation=^,  (77) 

«         '  t 

and  the  horizontal  line  be  is  readily  ob- 
tained. 

If  the  process  of  vaporization  is  not 
complete,  that  is,  if  the  final  quality  is 
less  than  unity,  heat  added  during  vapori- 
zation will  be  xr  and  then  the  entropy 
change  will  be 

^  =  ^-  (78) 

L  v 

The    horizontal    would    then   be    shorter 

jT 

and  would    really  be   -—    of    the    total 
100 

length  of  be,  as  can  readily  be  seen  by 
comparing  (76)  and  (77).  The  length  of 
the  line  for  any  case  divided  by  the  length 
be  must  then  be  a  measure  of  the  quality 
of  the  vapor. 


112 

For  the  line  cd  representing  superheat- 
ing, the  change  of  entropy  can  be  found 
by  means  of  equation  (53),  which  re- 
written to  suit  these  conditions  is 

<j>2  —  <£i  =  <£  8  =  change  during  superheating 

(79) 

The  specific  heat  of  steam  vapor  at  con- 
stant pressure  is  used  because  the  process 
of  vaporization  and  superheating  has  been 
considered  under  constant  pressure  condi- 
tions. It  is  of  course  possible  to  develop 
equations  for  conditions  of  variable  pres- 
sure, but  it  only  complicates  the  problem 
and  gives  results  which  are  not  required 
for  elementary  work. 

Summing  up,  the  total  entropy  of 
superheated  vapor,  considered  above  the 
arbitrary  zero,  32°  F.,  is 


(80) 


113 

and  when  the  vapor  is  wet-  instead  of 
superheated 


There  is  a  great  difference  in  the  way 
in  which  superheated  vapors  and  satu- 
rated vapors  behave  when  brought  into 
contact  with  the  liquid  form  of  the  same 
material.  Thus,  if  the  saturated  vapor  of 
a  liquid  be  brought  in  contact  with  that 
liquid  at  the  same  temperature  and  pres- 
sure, there  will  be  no  loss  of  heat  by  the 
vapor  and  it  is  said  to  be  in  thermal 
equilibrium  with  its  liquid.  On  the  other 
hand,  if  the  superheated  vapor  of  the 
same  liquid  be  brought  into  contact  with 
that  liquid  at  the  same  pressure  and  at 
the  temperature  of  vaporization,  the 
superheat  will  diminish.  That  is,  heat 
will  be  given  up  by  the  vapor  and  will 
be  absorbed  by  the  liquid  as  heat  of 
vaporization.  This  process  will  continue 
until  the  superheat  has  all  disappeared, 
leaving  a  saturated  vapor  mixed  with 


114 

that  generated  by  the  absorption  of  heat 
by  the  liquid;  or,  if  the  superheat  be 
great  enough  in  quantity,  until  the  liquid 
is  entirely  vaporized  and  the  resultant 
vapor  superheated  to  a  temperature  equal 
to  that  of  the  vapor  giving  up  heat.  A 
vapor  in  a  superheated  condition  cannot 
therefore  exist  in  the  presence  of  its 
liquid,  it  being  necessary  to  entirely 
vaporize  any  liquid  before  superheating 
can  begin.  This  is  recognized  by  saying 
that  a  superheated  vapor  is  not  in  thermal 
equilibrium  with  its  liquid. 

A  very  useful  curve  may  be  obtained 
by  plotting  the  specific  volumes  of  satu- 
rated vapors  against  the  corresponding 
pressures.  This  gives  what  is  called  the 
Saturation  Curve.  It  is  useful  as  indicat- 
ing the  volume  that  unit  weight  of  satu- 
rated vapor  will  have  at  any  given  pres- 
sure. For  steam  it  is  almost  perfectly 
expressed  by  the  equation 

=  constant  (82) 


through  the  common  temperature  ranges. 


115 

EVAPORATION. 

It  is  now  necessary  to  consider  what  is 
ordinarily  known  as  evaporation  of  a 
liquid.  Although  at  first  sight  it  appears 
very  different  from  the  vaporization  just 
discussed,  it  is  in  reality  the  same  thing. 
Vaporization  from  the  surface  of  a  liquid 
above  which  is  the  gas  of  another  substance 
does  not  take  place  under  the  pressure  of 
that  gas,  but  under  the  pressure  of  any 
vapor  of  the  evaporating  liquid  which  may 
be  present  and  be  mixed  with  the  gas.  Thus 
water  in  a  vessel  open  at  the  top  will 
evaporate  or  vaporize  in  the  same  way 
and  with  the  same  absorption  of  heat, 
and  in  the  same  quantity,  if  it  be  exposed 
to  still  ajr  or  other  similar  gas,  or  be 
exposed  to  a  space  devoid  of  air  or  other 
gas.  The  pressure  under  which  evapora- 
tion takes  place  is  that  of  the  water  vapor 
in  the  space  above  the  surface  of  the 
liquid,  and  if  there  happens  to  be  air  in 
that  space  the  phenomenon  of  evapora- 
tion is  not  altered.  For  very  exact 


116 

physical  work  this  statement  must  be 
modified  to  take  account  of  certain  varia- 
tions introduced  by  very  minute  molecular 
attractions  between  different  gases  and 
vapors,  but  for  the  most  exact  engineering 
work  the  law 'may  be  stated: 

Evaporation  from  the  surface  of  a  liquid 
in  contact  with  a  gds  or  gases  with  uh'ch 
the  liquid  or  its  vapor  does  not  react  chem- 
ically, is  independent  of  the  presence  of  that 
gas. 

Since  the  evaporation  of  liquid  takes 
place  under  the  pressure  of  the  vapor 
of  that  liquid,  the  latent  heat  of  vapori- 
zation and  similar  quantities  must  corre- 
spond to  that  pressure.  Such  heat  values 
can  easily  be  found  for  any  case  when  a 
vapor  table  for  that  particular-  substance 
is  at  hand,  because,  although  it  is  gener- 
ally difficult  to  measure  the  vapor  pres- 
sures, they  must  correspond  to  the 
temperatures  of  the  space  above  the 
liquid.  The  vapor  in  that  space  must  be 
saturated,  because  if  superheated  it  would 
lose  heat  to  the  liquid,  as  previously 


117 

described.  If  saturated,  its  pressure  must 
correspond  to  its  temperature,  and  know- 
ing the  latter,  the  former  can  be  found 
from  the  vapor  tables.  Thus,  water  with 
its  surface  exposed  to  air  at  a  tempera- 
ture of  t°  F.  will  evaporate  until  the 
space  above  it  contains  as  much  water 
as  it  is  capable  of  holding  at  that  tem- 
perature; that  is,  until  the  volume  occu- 
pied by  unit  weight  of  the  vapor  corre- 
sponds to  the  value  given  in  the  vapor 
tables.  The  water  vapor  must  have  the 
same  temperature  as  the  air  with  which 
it  is  mixed,  and  must  have  the  pressure 
corresponding  to  that  temperature  and 
also  contain  all  heat  in  quantities  corre- 
sponding to  that  temperature.  To  find 
heat  necessary  to  cause  evaporation  of 
one  pound  under  such  conditions,  the 
temperature  of  the  space  above  the  liquid 
must  be  found  in  the  steam  tables,  and 
the  corresponding  heat  of  vaporization  is 
the  value  sought. 


CHAPTER  VII. 

EXPANSIONS  AND  COMPRESSIONS  OF 
VAPORS. 

VAPORS  are  often  used  as  the  working 
substances  of  heax -engines  and  heat-pumps, 
because  when  subjected  to  heat  treatment 
they  undergo  volume  changes  similar  to 
those  of  gases.  The  laws  governing  the 
changes  are,  however,  very  different  from, 
and  not  quite  so  simple  as,  those  which 
have  been  formulated  for  the  perfect  gas. 

ISOTHERMAL   CHANGE   OF  VAPOR. 

An  Isothermal  or  Constant  Temperature 
Expansion  of  a  saturated  vapor  must  be  an 
expansion  at  constant  pressure  because 
the  pressure  cannot  change  without  a  change 
of  temperature.  Study  of  all  possibilities 
118 


119 

will  reveal  the  fact  that  the  only  way  in 
which  a  volume  of  saturated  vapor  can 
be  increased  while  its  pressure  remains 
constant  is  by  the  addition  of  more  vapor. 
In  the  case  of  a  gas,  one  pound  of  material 
at  a  given  temperature,  T,  can  have  any 
pressure  within  perfect  gas  limits  and 
corresponding  volume,  but  one  pound  of 
saturated  vapor  at  temperature  T  can 
have  only  one  pressure  and  one  volume. 

The  process  of  vaporization  which 
under  constant  pressure  occurs  at  con- 
stant temperature  is  called  the  Isothermal 
Expansion  of  saturated  vapor,  though  it 
might  more  correctly  be  called  the  Iso- 
thermal Formation  of  Vapor  from  Liquid. 
Corresponding  liquefaction  is  equivalent  to 
Isothermal  Compression.  The  isothermal 
line  of  a  saturated  vapor,  being  a  constant 
pressure  line,  must  be  a  horizontal  line 
on  the  PV  diagram.  It  is  convenient  to 
express  the  isothermal  by  means  of  an 
equation  of  the  form 

PVn  =  constant 


120 

as  before,  and  this  can  be  done  by  choos- 
ing a  proper  value  for  n.  Since  the  line 
is  a  constant  pressure  line, 

P= constant,  (83) 

and  a  value  of  n  must  be  found  which 
will  make  Vn  in  the  type  form  equal  to 
unity.  Obviously  n  must  equal  zero, 
and  the  Isothermal  Line  of  Saturated 
Vapor  is  given  by  the  equation 

PV°  =  constant.  (84) 


ADIABATIC  CHANGE   OF  VAPOR. 

Adiabatic  changes  of  vapor  are  more 
complicated  than  isothermal  changes, 
because,  in  a  way,  less  restricted.  If  a 
saturated  vapor  at  a  certain  temperature, 
T,  and  corresponding  pressure,  P,  be 
allowed  to  expand  without  reception  or 
rejection  of  heat,  the  increase  of  volume 
would  be  paralleled  by  a  decrease  of 
pressure  and  temperature.  Decrease  of 
temperature  and  pressure  will,  however, 


121 

cause  a  change  in  the  total  heat  necessary 
to  maintain  the  material  in  the  form  of 
a  saturated  vapor.  If  this  heat  is  less 
for  the  lower  pressures  than  for  the  higher 
initial  condition,  the  expanded  material 
will  contain  more  heat  than  is  necessary 
to  maintain  it  as  a  saturated  vapor  and 
it  will  become  superheated.  If  the  total 
heat  is  greater  at  low  than  at  high  tem- 
peratures, the  heat  contained  within  the 
expanding  material  will  not  be  sufficient 
to  maintain  it  all  in  the  condition  of 
saturated  vapor,  and  some  will  condense 
to  liquid  at  the  same  temperature  as  the 
vapor,  giving  up  its  latent  heat  of  vapori- 
zation to  that  material  remaining  in  the 
vaporous  state. 

Further,  if  the  vapor  be  required  to  do 
external  work  during  the  adiabatic  ex- 
pansion, it  must  supply  from  its  own 
stock  of  heat  a  quantity  equivalent  to 
the  work  done.  In  the  first  case  just 
considered  this  might  be  less  than  "the 
heat  liberated  by  drop  of  pressure,  so  that 
superheating  would  still  take  place  but 


122 

not  to  so  great  a  degree.  It  might  be  just 
equal  to  that  liberated,  under  which  con- 
ditions the  vapor  would  remain  dry 
during  the  entire  expansion.  Or  it  might 
be  greater  than  that  liberated,  so  that  a 
partial  condensation  would  have  to  take 
place  to  supply  the  extra  heat  needed. 

To  further  complicate  matters,  any 
liquid  which  is  condensed  has  a  tempera- 
ture equal  to  that  of  the  vapor  at  the 
instant  of  its  condensation.  It  therefore 
has  an  amount  of  heat  associated  with 
it  equal  to  the  heat  of  the  liquid  at  that 
temperature.  As  expansion  of  the  vapor 
continues,  its  pressure  and  temperature, 
and  the  heat  necessary  to  maintain  its 
liquid  under  its  pressure,  decrease.  The 
liquid  previously  condensed  will  there- 
fore have  to  partly  re  evaporate  and  by 
that  means  absorb  its  excess  heat,  or  give 
it  up  to  the  expanding  vapor  with  the 
same  result.  If  the  expanding  vapor 
contains  liquid  before  expansion  starts, 
matters  will  be  still  further  complicated 
by  re-evaporation  from  that  liquid. 


123 

It  can  readily  be  seen  that  this  set  of 
phenomena  may  lead  to  very  different 
conditions  for  different  vapors.  The  only 
way  in  which  results  may  be  arrived  at 
is  to  study  each  vapor  separately  and 
determine  physical  constants  to  be  used 
in  its  equations.  Steam  being  a  vapor 
which  has  been  much  used  by  engineers 
for  many  years,  most  of  its  constants  have 
been  accurately  determined,  and  it  will 
be  taken  as  an  example  in  illustrating  the 
way  in  which  the  laws  of  adiabatic  ex- 
pansion are  expressed. 

The  shape  of  curves  representing  adia- 
batic expansion  on  the  PV  diagram  will 
vary  with  the  initial  quality  o:  the 
vapor  at  the  instant  at  which  it  begins 
to  expand.  The  logarithmic  equation 

PVn  =  const  ant  (85) 

may  be  assumed  for  all  such  curves  and 
will  give  sensibly  correct  results  provided 
the  proper  values  of  n  are  used. 

Zeuner  found  that  for  steam  n  had  the 
following  values  for  the  initial  qualities 


124 

given,  when  dealing  with  ordinary  pres- 
sures: 

Initial  Quality.  Value  of  n. 

1.00 1.135 

.95 1.130 

.90 1.125 

.85 1.120 

.80 1.115 

.75 1.110 

.70...' 1.105 

Which  give  for  the  value  of  n  the  following 

equation: 

n=1.035  +  .lz,  (86) 

where  x  is  given  in  hundredths  and  not 
in  per  cent. 

The  T<j)  diagram  may  be  made  to  show 
very  clearly  the  various  changes  of 
quality  during  adiabatic  expansions  and 
compressions.  In  Fig.  15  the  line  ab 
represents  the  entropy  changes  of  water 
as  it  is  heated  to  various  temperatures. 
This  is  found  by  means  of  equation  (76) 
by  assuming  the  specific  heat  equal  to 
unity  and  putting  TV  equal  to  successively 
higher  values  corresponding  to  neces- 


125 

sarily  higher  pressures.  The  lines  be, 
b'c'  ,  b"c",  etc.,  represent  entropy  changes 
that  would  take  place  were  vaporization 
to  occur  at  any  of  the  temperatures  at 
which  they  are  drawn,  and  are  obtained 
by  equation  (77).  The  line  cc'"  is 
drawn  through  the  points  representing 
the  total  *  entropy  of  dry  and  saturated 
vapor  at  different  temperatures.  It  is 
obtained  by  adding  results  of  equations 
(76)  and  (77). 

As  previously  developed,  if  a  vapor  at 
temperature  TI  have  entropy  as  shown 
by  point  e,  then  it  must  be  a  wet  vapor 

consisting  of  —  -  pounds  of  vapor  and 
1UU 

—  ^  pounds  of  liquid.  The  quality  xe 
could  be  obtained  by  the  equation 


and  this  would  be  true  for  any  position  of 

the  point  e  between  the  lines  ab  and  cc'". 

Since  adiabatic  changes  are  represented 


126 

on  such  a  diagram  by  vertical  lines,  con- 
stant entropy  lines,  the  dotted  line  ee"f 
must  represent  an  adiabatic  expansion. 
It  can  be  readily  seen  that  in  the  case 
of  water  vapor,  for  which  this  diagram 

v.     be  Ve'   We" 
was  drawn,  the  quality-,  — ,  — ,  etc., 

decreases  as  expansion  continues.  If 
expansion  had  started  at  /,  about  half- 
way between  b  and  c,  representing  a 
quality  of  50%,  the  diagram  shows  that 
the  quality  would  have  remained  nearly 
constant.  Expansion  starting  at  g,  with 
quality  lower  than  50%,  shows,  an  im- 
provement in  quality  as  expansion  pro- 
ceeds. These  results  are  of  course  true 
for  steam  only;  to  determine  correspond- 
ing laws  for  other  vapors,  similar  diagrams 
would  have  to  be  constructed  for  them  and 
their  laws  developed  individually.  This 
serves,  however,  to  indicate  the  very 
convenient  and  simple  method  which 
the  conception  of  entropy  gives  for  de- 
termining laws  of  materials  of  very  com- 
plex behavior. 


CHAPTER  VIII. 
VAPOR   CYCLES. 

As  in  the  case  of  gas-engines,  the  Carnot 
cycle  is  used  as  the  standard  of  excellence 
for  vapor  engines.  Due,  however,  to  the 
peculiar  properties  of  vapors,  the  shape 
of  the  Carnot  cycle  for  such  working 
substances  is  different  from  that  already 
studied.  Remembering  that  it  consists 
of  two  isothermals  crossed  by  two  adia- 
batics,  and  that  isothermals  for  vapors 
are  constant  pressure  processes,  the  reason 
for  the  main  difference  in  shape  is  appar- 
ent. 

CAENOT  CYCLE  FOR  VAPOR. 

If,  in  Fig.  16,  the  volume  Va  be  taken 
to  represent  that  of  one  pound  of  mixed 
127 


128 


liquid  and  vapor  at  pressure  Pa,  the 
addition  of  heat  will  cause  further  vapori- 
zation at  constant  temperature.  This  will 
be  an  isothermal  expansion  continuing  to 


a    b 


FIG.   16. 

some  point,  b,  with  partial  or  total  va- 
porization. Adiabatic  expansion  will  then 
take  place  according  to  the  law 

PVn  —  constant, 


129 

but  n  will  have  a  value  dependent  upon 
the  initial  quality  at  6.  Thus  with  steam, 
if  the  quality  at  b  were  100%,  Zeuner's 
equation  of  be  would  be 


5  =  constant, 
and  if  xb  were  equal  to  75%, 
PF1110  =  constant 

would  give  the  line  be. 

The  line  cd  represents  partial  condensa- 
tion until  the  volume  Va  is  reached,  when 
adiabatic  compression  will  bring  it  back 
to  the  condition  of  mixed  vapor  and 
liquid  at  pressure  Pa  and  volume  Va. 

The  heat  supplied  along  ab  will  be  the 
difference  between  total  heat  in  the 
material  at  a  and  b.  Thus, 

Qi  =  (xtfb  +  ft)  -  (xaTa  +qa)  =  xbrb  -  xara 
=  ra(xb-xa).  (88) 

Similarly  the  heat  rejected  along  cd  will 
be  the  amount  of  latent  heat  given  up,  • 
and  since  there  may  be  any  quality  at  c 


130 

and  any  other  quality  less  than  that  at 
d,  the  expression  is  similar  to  the  above: 

Q2  =  Xcrc-Xdrd  =  rc(xc-xd).       (89) 

The  work  done  during  the  isothermal 
expansions  and  compressions  is  given  by 
the  type  formula  of  equation  (6),  and  that 
during  adiabatic  changes  by  the  first  part 
of  equation  (40).  The  first  part  of  the 
latter  equation  was  developed  without 
making  use  of  properties  peculiar  to  per- 
fect gases  and  will  hold  for  any  material 
for  which  it  can  be  said  that  PVn  is 
constant  during  an  adiabatic  change. 

A  table  can  then  be  constructed  similar 
to  that  used  in  the  case  of  the  Carnot  cycle, 
with  gas  for  working  substance,  as  fol- 
lows: 


Line. 

Heat  Received. 

Work  Done. 

ab 

+ra(xb—Xa) 

+Pa(Vb-Va) 

be 

0 

,  PbVb-PcVc 

T"                     -, 

n  —  1 

cd 

-rc(xc-xd) 

-Pc(7c-Fd) 

da  0 

n  —  l 


131 


132 

From  this  the  following  rather  compli- 
cated expression  for  efficiency  is  readily 
obtained  : 


Pa(Vb-  Va)  +    bb~_c  -  Pc'Vc-  Vd) 

PgVa-PdVd 

Eff.=  -  —  2=1  - 
ra(xb-Xa) 

(90) 

or,  expressing  it  in  a  different  way, 
™      Qi-Q2__ra(xb-Xg)-rc(xc-Xd)  /A1N 

Hill.  --  7^  -  --  —  ~f  -  r  -  •W-U 

Ql  ra(Xb-Xa) 

Either  of  the:e  can  be  still  further  sim- 
plified, but  as  the  process  is  rather  com- 
plicated and  the  same  result  can  be 
much  more  easily  obtained  from  the  T<p 
diagram,  the  latter  method  will  be  used. 

Drawing  the  Carnot  cycle  to  T<f>  co- 
ordinates it  has  the  appearance  shown 
in  Fig.  17,  having  exactly  the  same  shape 
as  that  obtained  when  using  gas  as 
working  substance.  The  area  under  the 
lineafr  representing  heat  supplied,  and  the 


133 

area  of  the  cycle  representing  heat  con- 
verted into  work,  the  efficiency 


It  will  immediately  be  noticed  that  this 
efficiency  is  the  same  as  that  obtained 
when  using  a  perfect  gas,  and,  although 
the  proof  of  such  a  statement  is  beyond 
the  limits  of  this  book,  the  Carnot  effi- 
ciency is  the  same  for  all  working  sub- 
stances no  matter  what  their  properties. 

Since 

Work  =  Heat  supplied  X  Efficiency, 

the  work  resulting  from  the  operation  of 
the  Carnot  cycle  with  vapor  is 


(93) 


The  Carnot  cycle  has  not  been  used  in 
any  practical  vapor  engine,  but  several 
such  engines  operate  with  cycles  very 


134 


similar  to  that  of  Carnot.  The  so-called 
"Clausius  Cycle/'  which  is  that  of  the 
modern  steam-turbine,  is  an  illustration 
of  a  practical  cycle  obtained  by  slight 
modification  of  Carnot's. 


CLAUSIUS   CYCLE. 

Drawn  on  the  PV  diagram,  this  cycle 
has  the  shape  shown  in  Fig.  18.  Assume 
the  volume,  Vaj  to  represent  that  of  one 
pound  of  liquid  at  the  temperature  of 
vaporization,  corresponding  to  the  pres- 
sure Pa.  The  addition  of  heat  will 
cause  isothermal  vaporization  or  expan- 
sion until  some  point,  fr,  is  reached,  at 
which  time  the  vapor  will  have  a  quality, 
xb,  equal  to  or  less  than  unity.  Adia- 
batic  expansion  will  then  bring  the  mate- 
rial to  Vc  with  a  pressure,  Pc,  at  which 
point  condensation  may  be  made  use  of 
to  bring  the  material  back  to  the  liquid 
state  at  the  same  pressure,  Pc  or  Pd,  and 
with  volume,  V&,  practically  equal  to  Va, 
since  the  expansion  of  liquids  through 


135 


ordinary  temperature  ranges  is  negligible 
when  compared  to  the  vapor  volume 
changes.  The  line  da  may  then  be 


a    b 


FIG.  18. 

assumed  a  constant  volume  or  vertical 
line,  and  represents  the  raising  of  pressure 
and  temperature  of  the  liquid  from  con- 
ditions at  d  to  those  at  a. 

The  heat  above  32°  F.  contained  in  the 


136 

liquid  at  Va  will  be  ga,  corresponding  to 
the  pressure  Pa.  That  in  the  material  at 
b  will  be  qa  +  xbrb,  and  rb  will  of  course 
correspond  with  the  pressure  Pb  or  Pa. 
At  the  end  of  the  expansion  the  heat  con- 
tained will  be  xcrc  +  qc,  and  after  condensa- 
tion the  heat  remaining  in  the  material 
will  be  qa  equal  to  qc.  During  the  process 
of  raising  the  pressure  from  d  to  a,  an 
amount  of  heat  equal  to  the  difference 
between  qa  and  qd  must  be  added,  and 
when  it  is  observed  that  this  heat  is 
added  at  temperatures  varying  from  the 
lowest  to  the  highest,  the  reason  why 
this  cycle  is  less  efficient  than  the  Carnot 
is  immediately  evident. 

The  energy  developed  by  the  engine, 
as  in  previous  cases,  is 


b-xcrc,  (94) 
and  the  efficiency  of  the  engine  is 

c 

.     iyO) 


qa  -  3d)  +  xbrb  -  xcrc 


-  -  -  —  ; 

(qa-q<i)+xbrb 


137 


138 

An  expression  for  the  energy  made 
available  may  be  obtained  by  adding 
algebraically  the  work  done  upon  each 
tine  of  the  cycle,  giving,  in  ft.-lbs. 


(96) 


The  efficiency  is  then  equal  to 


- 

Eff  .  =  4 
J 


(97) 


The  !T<£  diagram  for  the  Clausius  Cycle, 
Fig.  19,  shows  plainly  why  it  is  less 
efficient  than  the  Carnot,  the  line  da 
being  substituted  for  the  lines  da'  and  a'  a. 
The  straight  lines  of  this  cycle  are  easily 
plotted  as  in  previous  cases,  and  the 
curved  line  da  is  the  same  as  the  line  ab 
of  Fig.  15. 


139 

RANKINE   CYCLE. 

Another  vapor  cycle  of  great  interest 
is  known  as  the  Rankine  cycle.  It  is 
the  ideal  form  of  the  cycle  upon  which 
the  ordinary  reciprocating  steam-engine 
works.  Its  shape  on  the  PV  diagram  is 
shown  bv  Fig.  20.  As  can  be  seen,  it 
differs  from  the  Clausius  Cycle  only  in 
having  the  "  toe  "  cut  off  by  the  vertical 
line  cd.  Its  efficiency  is  naturally  less 
than  that  of  a  Clausius  Cycle  with  the 
same  pressure  limits,  because,  while  the 
same  amount  of  heat  is  received  along  the 
lines  ea  and  afr,  the  work  done  is  less  by 
the  area  beyond  cd.  This  area  is  spoken 
of  as  representing  work  lost  by  incomplete 
expansion. 

The  output  of  mechanical  energy  is  given 
by  an  expression  of  exactly  the  same 
form  as  equation  (90) ;  thus, 

Output  =  E  =  Qi-Q2,  (98) 

which  is  less   than  the  available  output 
of    the   Clausius   Cycle,  because   in   this 


140 

case  Pc  has  a  greater  numerical  value. 
The  efficiency  is 


Eff.-- 


(99) 


FIG.  20. 


141 

Both  of  these  expressions  give  results 
smaller  than  those  of  the  Clausius  Cycle, 
because  $2,  the  quantity  of  heat  ex- 
hausted, is  larger  in  the  case  of  the 
Rankine  for  similar  pressures.  This  is 
plainly  evident  when  it  is  observed  that 
at  the  end  of  the  adiabatic  expansion 
at  pressure  Pc  condensation  must  take 
place  with  a  rejection  of  heat  to  give  the 
const  ant- volume  pressure  drop,  while  in 
the  Turbine  Cycle  no  heat  is  rejected  until 
the  pressure  has  dropped  to  the  lowest 
point  of  the  cycle.  The  difference  in 
the  value  of  Q2  for  the  two  cases  is 
plainly  the  difference  in  total  heat  of 
the  vapor  at  pressures  Pc  and  Pd  of 
Fig.  20. 

Expressions  for  work  and  efficiency  of 
the  Rankine  Cycle  similar  to  (92)  and 
(93)  are  as  follows: 


142 
and 


(101) 

The  T<p  diagram  for  this  cycle  having 
the  shape  drawn  in  Fig.  21  plainly  shows 
the  fact  that  it  is  still  less  efficient  than 
that  of  Clausius,  both  being  compared 
with  the  Carnot  Cycle  as  standard. 

With  the  exception  of  cd,  all  of  the 
lines  of  this  diagram  are  obtained  exactly 
as  are  those  of  Fig.  19.  The  line  cd  is 
constructed  by  taking  cognizance  of  the 
fact  that  it  represents  T$  variations  dur- 
ing a  constant-volume  change,  as  shown 
by  cd  of  Fig.  20.  During  this  volume 
change  the  pressure  and  temperature  drop, 
and  therefore  the  volume  occupied  by  a 
given  weight  of  vapor  would  tend  to  in- 
crease. Since,  however,  the  volume  is 
maintained  constant  by  the  piston  re- 
maining stationary  at  the  end  of  the  stroke, 
the  total  weight  of  steam  remaining  in  the 
vaporous  condition  must  be  constantly 


143 


144 

growing  less.     That  is,  condensation  must 
be  taking  place. 

The  volume,  Vc,  is  known,  and  the 
vapor  tables  give  the  volume  which  one 
pound  of  vapor  would  occupy  if  dry  and 
saturated  at  the  pressure  Pc.  Assuming 
unit  weight  of  working  substance  and 
neglecting  the  volume  of  liquid  present 
at  C  as  very  small  compared  with  the 
volume  of  vapor,  the  quality  is 


where  Vc  is  the  volume  per  pound  of  dry 
and  saturated  vapor  at  pressure  Pc. 
For  any  weight  of  working  substance  other 
than  unity,  it  is  only  necessary  to  mul- 
tiply Vc  in  (101)  by  the  number  of 
pounds  of  material  present.  At  any 
later  time,  when  the  pressure  has  dropped 
to  PC',  the  specific  volume  V'c  above 
will  have  changed  to  some  new  and  larger 
volume,  Vfc',  and  the  quality  will  be 
V*> 


145 

so  that  the  quality  may  be  very  approxi- 
mately found  for  any  point  on  the  line 
cd  of  Fig.  20. 

As  was  developed  in  connection  with 
Fig.  15,  the  point  c  of  Fig.  21  divides  the 
line  fg  in  such  a  way  that 

jjj=xc;  (103) 

and  since  the  quality  at  any  point  of  the 
line  cd  can  be  found  by  the  method  out- 
lined in  the  last  paragraph,  the  length 
of  the  line  dg''  for  any  position  is  easily 
determined,  because 

f—-x* 

giving 

fc'=x«-f'g'  (104) 

for  any  position  which  may  be  selected. 
Therefore  by  choosing  enough  positions 
for  the  point  c',  a  sufficient  number  of 
lengths  c'g'  may  be  calculated  to  rriake 
possible  the  plotting  of  the  line  cd,  after 


146 

which  the  cycle  continues  along  the  same 
horizontal  line  as  is  used  in  the  Clausius 
Cycle. 

The  Rankine  Cycle  is  often  modified 
in  practice  by  adding  more  heat  along 
the  line  ab  than  is  required  to  form  dry 
and  saturated  vapor.  The  result  is  the 
superheating  of  the  material  after  com- 
plete evaporation  and  then  the  ac!iabatic 
expansion  starts  with  this  superheated 
vapor.  The  T$  diagram  for  such  a  case 
is  shown  in  Fig.  22,  in  which,  v/ith  the 
exception  of  the  curve  bb',  all  the  lines 
are  similar  to  those  of  Fig.  21.  The 
curve  W,  which  represents  the  super- 
heating of  the  vapor  at  const  ant  pressure, 
is  obtained  by  means  of  equation  (78). 
The  adiabatic  expansion  is  a  vertical  line 
from  the  point  b'  down  to  the  point  which 
gives  the  desired  temperature  and  corre- 
sponding pressure.  The  point,  n,  in  which 
b'c  crosses  bg  gives  the  temperature  at 
which  the  expanding  material  will  just 
reach  the  dry  and  saturated  condition. 
If  expansion  continues  beyond  this  point 


147 


the  quality  will  constantly  decrease  until 
the  partial  condensation  at  constant 
volume  begins  at  c.  It  is  readily  seen 


I 


from  the  dotted  lines  on  the  figure  what 
an  enormously  high  degree  of  superheat 
would  have  to  be  used  to  just  give  dry 


148 

and  saturated  steam  at  the  end  of  ex- 
pansion. 

VAPOR   REFRIGERATING-MACHINES. 

Many  refrigerating-machines  are  oper- 
ated with  vapors  as  the  working  substance. 
The  reversed  Carnot  Cycle  could  be  used 
for  such  purposes,  but  it  introduces 
certain  complications  of  apparatus  and 
has  been  considered  undesirable  in  prac- 
tice. The  most  common  cycle  is  one 
having  the  shape  of  the  Clausius  but 
operated  of  course  in  the  opposite  direc- 
tion. 

Starting  with  a  volume  of  liquid,  Vd 
in  Fig.  18,  behind  a  piston,  evaporation 
is  allowed  to  take  place  as  the  piston 
moves  out  until  the  vapor  or  mixture  of 
vapor  and  liquid  finally  occupies  a  volume 
Vc.  During  this  process  the  latent  heat 
of  vaporization  is  absorbed  from  the  cold 
body,  the  one  which  is  to  be  cooled  in 
the  ordinary  practical  case.  The  vapor, 
dry  or  wet,  is  then  compressed  adiabat- 


149 

ically  until  some  pressure,  Pb,  is  reached, 
when  condensation  at  constant  pressure 
is  effected.  This  is  done  by  removing  the 
latent  heat  of  vaporization  corresponding 
to  the  pressure  Pb  or  Pa,  that  is,  dis- 
charging it  into  the  hot  body.  From  a 
to  d  the  pressure  is  dropped  at  practically 
constant  volume,  which  means  that  the 
heat  of  the  liquid)  qa—<ld,  must  be  given 
up  in  some  way. 

Analysis  of  this  cycle  by  means  of  the 
T(j>  diagram  given  in  Fig.  19  is  a  very 
simple  matter. 

Starting  at  d,  heat  is  absorbed  during 
the  vaporization  dc.  The  quantity  of 
heat  absorbed  during  this  process  is  repre- 
sented by  the  area  dcef.  Then  adiabatic 
compression  raises  the  temperature  from 
Tc  to  Tfc,  after  which  condensation  gives 
to  the  hot  body  the  amount  of  heat 
represented  by  the  area  bage.  The  liquid 
must  then  be  lowered  in  temperature 
from  Ta  to  Td  and  this  is  done  by  allow- 
ing it  to  give  to  the  cold  body  an  amount 
of  heat  adfg. 


150 

The  result  of  the  operation  of  the  cycle 
is  then  the  removal  from  the  cold  body 
of  an  amount  of  heat  dcef  and  the  relurn 
to  it  of  an  amount  adfg,  so  that  the  actual 
refrigeration  or  net  heat  removal  is  the 
amount  of  heat 

Q2  =  dcef-adfg.  (105) 

This  is  accomplished  by  an  expenditure 
of  work  equal  in  thermal  units  to  the 
area  dcbad. 

Expressing  these  areas  in  terms  of  heat 
quantities  gives 

Area  dcef  represents  xcrc] 
Area  adfg  represents  qa  —  q<i', 
Area  dcbad,  equal  to  bage+adfg—dfec, 
represents  xbrb  +  (qa  -  qd)  -  xcrc. 

Therefore  the  actual  heat  removed  from 
the  cold  body 

Q2  =  xjrc-(qa-qa),  (106) 

and  the  work  expended,  expressed  in 
thermal  units,  is 

E  =  xbrb  +  qa-qd-  xcrc.          (107) 


151 

The  heat  given  to  the  hot  body  is  of 
course  the  sum  of  heat  absorbed  from 
the  cold  body  and  work  put  into  the 
mechanism,  giving 


as  previously  developed. 
If  the  efficiency  be  taken  as 

Tpff  _Heat  removed  from  cold  body 
Work  expended 

the  value  for  this  case  becomes 


. 

xbrb-xcrc+(qa-qd) 

which  obviously  can  have  any  valua 
greater  or  less  than  unity  depending  only 
upon  the  relative  values  of  the  heat 
quantities.  From  Fig.  19  it  is  evident 
that  the  steeper  the  line  da,  the  greater 
will  be  the  amount  of  heat  removed  for  a 
given  temperature  and  pressure  range 
in  the  apparatus;  or,  the  greater  the 


152 

length  of  ab  as  compared  with  dc,  the 
greater  will  be  the  amount  of  heat  re- 
moved. It  is  therefore  desirable  in 
practice  to  use  materials  which  have 
large  latent  heats  of  vaporization  and 
small  specific  heats  when  in  the  liquid 
form. 

Certain  peculiarities  of  this  cycle  may 
now  be  noticed.  Vaporization  could  be 
continued  beyond  c  to  a  point  c',  such 
that  the  adiabatic  compression  would 
just  give  dry  and  saturated  vapor  at  the 
pressure  P&.  Or  vaporization  could  be 
continued  to  a  point  c",  such  that  adia- 
batic compression  would  superheat  the 
material  to  temperature  Tk,  so  that  as 
the  removal  of  heat  took  place  the  super- 
heated vapor  would  first  cool  along  a  line 
Kb  and  then  condense  along  the  line  ba 
as  before.  If  points  c,  c',  and  c"  be  so 
chosen  that  areas  cc'e'e  and  c'c'W  are 
equal,  it  can  easily  be  seen  that  more  area 
is  given  to  the  card  to  obtain  the  second 
than  the  first  of  the  two  equal  areas. 
That  means  more  work  must  be  done  for 


153 

a  given  amount  of  refrigerating  or  cooling, 
when  superheating  takes  place.  For  thie 
reason  the  practical  machines  when  operat* 
ing  upon  this  cycle  always  compress  a 
wet  rather  than  a  dry  vapor. 


CHAPTER  IX. 
FLOW  OF  VAPOR. 

THE  formulas  developed  for  the  flow  of 
gases  from  one  reservoir  to  another  were 
made  dependent  upon  the  truth  of  equa- 
tion (66),  which  is  merely  another  form 
of  the  following  expression: 


V,2  VJ 

=J(S2+I2+E2)  +L. 


This  equation  is  of  course  equally  true 
for  vapors,  being  simply  an  algebraic 
statement  of  the  fact  that  if  no  energy 
transfer  takes  place  by  radiation  and 
other  lo:ses,  the  sum  of  all  the  energies 
associated  with  a  body  at  the  end  of  an 
operation  must  equal  the  sum  of  those 
154 


with  which  it  started.     Beginning  with  it 
as  a  basis  and  neglecting  vi  as  before, 


and 
and 


for  wet  or  dry  saturated  vapors,  so  that 


W(Q.-Q2)  (109) 

and 


va=\  2;J(Q  -Q2) 

=V/2jJ{(x^+q)-(x22  +  q2)},  (110) 

where  subscript  d)  denotes  conditions 
in  the  reservoir  from  which  flow  takes 
place,  and  subscript  (2)  is  used  to  desig- 
nate the  conditions  within  the  nozzle  at 
the  point  at  which  the  maximum  velocity 
is  attained. 


156 

Equation  (111)  can  be  modified  to  take 
into  account  superheated  condition  of 
the  vapor.  Thus  for  initial  superheat 
but  a  wet  final  condition 


(xaru  +  qa)},      (111) 

and    for    initial    and    final    superheated 
conditions, 


(112) 

Inspection  of  (110),  (111),  and  (112) 
shows  that  a  knowledge  of  the  quality 
of  the  material  at  the  end  of  expansion 
is  necessary,  and  this  is  readily  obtained 
by  means  of  the  T<f>  diagram,  as  already 
shown.  Drawing  a  vertical  line  on  such 
a  diagram  from  any  initial  conditions  will 
give  the  final  conditions  of  an  adiabatic 
expansion  down  to  any  set  of  terminal  or 
final  values  which  may  be  selected. 

Experiment  shows  that  with  vapors,  as 
with  gases,  the  nozzle  pressure  will  de- 


157 

crease  as  the  external  pressure  decreases, 
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P2,  is  reached,  and  this  cannot  be  further 
lowered  by  any  decrease  of  external 
pressure.  This  minimum  value  of  P2  in 
the  case  of  steam  is  about  0.58Pi,  and 
gives  a  velocity  of  about  1400  ft.  per 
second,  in  the  average  case. 


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10  D.    VAN    NOSTRAND   COMPANY^ 


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CLAPPERTON,   G.      Practical    Paper-making.      A 

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CLARK,  D.  K.,  C.E.     A  Manual  of  Rules,  Tables 

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12  D.  VAN   NOSTRAND  COMPANY^ 


Tramways;  Their  Const rwctHm  and  Working. 

Embracing  a  comprehensive  history  of  the 
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CLEEMANN,    T.     M.       The    Railroad    Engineer's 

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CLEVENGER,   S.   R.      A   Treatise   on   the   Method 

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14  t>.    VAtt    NOSTRAttD  COMPANY^ 


CROCKER,   F.    B.,    Prof.      Electric    Lighting.      A 

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Engineers,  Students',  and  others  interested  in 
the  Installation  or  Operation  of  Electrical 
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8vo,    cloth,    illustrated    $3.00 

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CROSSKEY,  L.  R.  Elementary  Perspective:  Ar- 
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Arranged  to  meet  the  requirements  of  Archi- 
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DAL.BY,    H.    A.      Rules    and    Dispatching,    Train. 

Leather.      Pocket   size    $1.50 

DAVIES,    E.     H.       Machinery     for     Metalliferous 

Mines.  A  Practical  Treatise  for  Mining  En- 
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With  upwards  of  400  illustrations.  Second 
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D.   C.     A  Treatise  on   Metalliferous   Minerals 

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SCIENTIFIC  PUBLICATIONS.  iS 


scented  soaps,  and  their  production  and  tests 
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DENNY,    G.    A.      Deep-level    Mines    of   the    Rand, 

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tical Manual.  Pocket  Size.  Oblong,  cloth. 
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$1.50 

DIBDIN,    W.    J.       Public    Lighting;    by    Gas    and 

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DIETERICH,    K.      Analysis    of    Resins,   Balsams, 

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raphy. Translated  from  the  German,  by  Chas. 
Salter.  8vo,,  cloth  net,  $3.00 

DINGER,  H.  C.,  Lieut.,  TJ.S.N.     Handbook  for  the 

Care  and  Operation  of  Naval  Machinery.  12mo, 
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DOBLE,  W.  A.     Power  Plant  Construction  on  the 

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DODD.  Geo.  Dictionary  of  Manufactures,  Min- 
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16  D.   VAN    NOSTRAND   COMPANY'S 


DORR,  B.  F.     The   Surveyor's   Guide  and  Pocket 

Table-book.  Fifth  Edition,  thoroughly  revised 
and  greatly  extended.  With  a  second  appendix 
up  to  date.  16mo,  morocco  flaps  $2.00 

DRAPER,    C.   H.      An    Elementary    Text-book    of 

Light,  Heat  and  Sound,  with  Numerous  Ex- 
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Heat   and  the   Principles   of   Therm o-clynnm- 

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DUCKWAL.L,,  E.  W.     Canning  and  Preserving  of 

Food  Products  with  Bacteriological  Technique. 
A  practical  and  scientific  handbook  for  Manu- 
facturers of  Food  Products,  Bacteriologists, 
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Gas  Residuals  and  By-Products,  and  Paper- 
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ECCLES,    R.   G.    (Dr.),    and    DTJCKWAL.L,,   E.   W. 

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retical Side  of  the  Pure  Food  Problem.  8vo, 

paper    $0 . 50 

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25 


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SCIENTIFIC   PUBLICATIONS.  27 


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SCIENTIFIC  PUBUCATIONS.  29 


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JANNETTAZ,  E.     A  Guide  to  the  Determination 

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SCIENTIFIC  PUBLICATIONS.  31 


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JONES,     H.     C.       Outlines     of     Electrochemistry. 

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KENNEDY,  R.  Modern  Engines  and  Power  Gen- 
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SCIENTIFIC   PUBLICATIONS.  33 


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of  a  Century.  Comprising  a  Large  Selection 
of  Tabulated  Results,  showing  the  Strength 


34  D.    VAN    NOSTRAND   COMPANY'S 


and  other  Properties  of  Materials  used  in  Con- 
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KOESTER,  F.     Steam-Electric  Power  Plants  and 

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SCIENTIFIC   PUBLICATIONS.  35 


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36  D.    VAN    NOSTRAND   COMPANY^ 


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LOCKE,  A.  G.  and  C.  G.     A  Practical  Treatise  on 

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"     A   Theoretical  and  Practical  Treatise   on  the 

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L.UPTON,   A.,   PARR,   G.  D.   A.,   and   PERKIN,   H. 

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MACKIE,    John.      How    to    Make    a    Woolen    Mill 

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SIARKS,  E.  C.  R.     Notes  on  the  Construction  of 

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SCIENTIFIC   PUBLICATIONS.  39 

Notes   on   the   Construction   and   Working   of 

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MARSH,  C.  F.,  and  DUNN,  W.  Reinforced  Con- 
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MAURICE,    WM.       Electric    Blasting    Apparatus 

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McINTOSH,  J.  G.  Technology  of  Sugar.  A  Prac- 
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40  D.   VAN    NOSTRAND   COMPANY'S 


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MERRITT,  Wm.  H.     Field  Testing  for  Gold  and 

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M1CHELL,  S.     Mine  Drainage;  being  a  Complete 

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MIERZINSKI,  S.,  Dr.     Waterproofing  of  Fabrics. 

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MILLER,  E.  H.    (Columbia   Univ.).     Quantitative 

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SCIENTIFIC  PUBLICATIONS.  41 


MIXIFIE,  \V.  Mechanical  Drawing.  A  Text- 
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Geometrical    Drawing.      Abridged    from    the 

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MODERN     METEOROLOGY.       A     Series     of     Six 

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MOORE,  E.  C.   S.      New  Tables  for  the   Complete 

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MOREING,    C.   A.,   and    NEAL,   T.      New    General 

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MOSES,   A.  J.      The   Characters   of   Crystals.      An 

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42  D.    VAN    NOSTRAND    COMPANY'S 


The    Lay-out    of    Corliss    Valve    Gears.    (Van 

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with  a  large  collection  of  original  and  care- 
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MUNRO,    J.,    C.E.,    and    JAMIESON,    A.,    C.E.      A 

Pocket-book  of  Electrical  Rules  and  Tables 
for  the  use  of  Electricians  and  Engineers. 
Sixteenth  Edition,  revised  and  enlarged.  With 
numerous  diagrams.  --  Pocket  size.  Leather. 
$2.50 

MURPHY,  J.  G.,  M.E.     Practical  Mining:.     A  Field 

Manual  for  Mining  Engineers.  With  Hints  for 
Investors  in  Mining  Properties.  16rao,  cloth. 
$1.00 

NAQUET,  A.     Legal  Chemistry.     A  Guide  to  the 

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cal Substances,  Analysis  of  Ashes,  and  Exami- 
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plied to  Chemical  Jurisprudence,  for  the  use  of 
Chemists,  Physicians,  Lawyers,  Pharmacists 
and  Experts.  Translated,  with  additions,  in- 
cluding a  list  of  books  and  memoirs  on  Toxi- 
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Ph.D.,  M.D.,  LL.D.  12mo,  cloth  $2.00 

NASMITH,    J.      The    Student's    Cotton    Spinning;. 

Third  Edition,  revised  and  enlarged.  8vo, 
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NEUBERGER,  H.,  and  NOALHAT,  H.  Technol- 
ogy of  Petroleum.  The  Oil  Fields  of  the 
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Annual  Production,  Prospection  and  Devel- 
opment; Oil-well  Drilling;  Transportation  of 
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Translated  from  the  French  by  John  Geddes 
8vo,  sloth,  illustrated,  net,  $10,00 


SCIENTIFIC  PUBLICATIONS.  43 


NEWALL,  J.   W.      Plain  Practical   Directions*   for 

Drawing,  Sizing  and  Cutting  Bevel-gears, 
showing  how  the  Teeth  may  be  cut  in  a  Plain 
Milling  Machine  or  Gear  Cutter  so  as  to  give 
them  a  correct  shape  from  end  to  end;  and 
showing  how  to  get  out  all  particulars  for 
the  Workshop  without  making  any  Drawings* 
Including  a  Full  Set  of  Tables  of  Reference, 
Folding  plates.  8vo,  cloth  $1.50 

NEWLANDS,    J.       The    Carpenters'    and    Joiners' 

Assistant:  being  a  Comprehensive  Treatise  on 
the  Selection,  Preparation  and  Strength  of  Ma- 
terials, and  the  Mechanical  Principles  of 
Framing,  with  their  application  in  Carpentry, 
Joinery  and  Hand-railing;  also,  a  Complete 
Treatise  on  Sines;  and  an  Illustrated  Glossary 
of  Terms  used  in  Architecture  and  Building. 
Illustrated.  Folio,  half  morocco  915.00 

NIPHER,  P.  E.,  A.M.  Theory  of  Magnetic  Meas- 
urements, with  an  Appendix  on  the  Method  of 
Least  Squares.  12mo,  cloth  $1.00 

NISBET,  H.     Grammar  of  Textile  Design.     With 

many  diagrams  and  figures.  8vo,  cloth,  illus- 
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NOLL,    Augustus.       How    to    Wire    Buildings:    A 

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many  illustrations.  Fourth  Edition.  8vo, 
cloth,  illustrated  $1.50 

NUGENT,  E.     Treatise  on   Optics;   or,  Light  and 

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trial Pursuits.  With  103  illustrations.  12mo, 
cloth  $1.50 

O'CONNOR,  H.     The  Gas  Engineer's  Pocket-hook. 

Comprising  Tables,  Notes  and  Memoranda  re- 
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Use  of  Coal-gas  and  the  Construction  of  Gas- 
works. Second  Edition,  revised.  12mo,  full 
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OLSEN,  J.   C.,   Prof.      Text-hook   of   Quantitative 

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With  Seventy-two  Laboratory  Exercises  giv- 
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vised. 8vo,  cloth  net,  $4.80 

OSBORN,   F.   C.      Tables   of   Moments   of   Inertia, 

and  Squares  of  Radii  of  Gyration;  supple- 
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Strength  of  Wrought-iron  Columns,  Safe 


44 


D.    VAN    NOSTRAND   COMPANY  S 


Strength  of  Timber  Beams,  and  Constants  for 
readily  obtaining  the  Shearing  Stresses,  Reac- 
tions and  Bending  Moments  in  Swing  Bridges. 
Fifth  Edition.  12mo,  leather  net,  $3.00 

OUDIN,    M.    A.      Standard    Polyphase    Apparatus 

and  Systems.  With  many  diagrams  and  fig- 
ures. Fifth  Edition,  revised  and  enlarged. 
Fully  illustrated.  8vo,  cloth,  370  pp.  ...$3.00 

PALAZ,  A.,  Sc.D.  A  Treatise  on  Industrial  Pho- 
tometry, with  special  application  to  Electric 
Lighting.  Authorized  translation  from  the 
French  by  George  W.  Patterson,  Jr.  Second 
Edition,  revised.  8vo,  cloth,  illustrated,  $4.00 

PAMELY,   C.      Colliery  Manager's   Handbook.      A 

Comprehensive  treatise  on  the  Laying-out  and 
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of  reference  for  colliery  managers  and  for 
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PARRY,  E.  J.,  B.Sc.     The  Chemistry  of  Essential 

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of  the  published  facts  connected  with  the  sub- 
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Essential  Oils.  With  numerous  diagrams  and 
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and    COSTE,   J-  H.      Chemistry   of   Pigments. 

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ous Occupations  and  their  Prevention.  A  book 
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PARSHAL.L,,  H.  P.,  and  HOBART,  H.  M.  Arma- 
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Electric  Railway  Engineering.  With  num- 
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cloth,   463    pp.,   illus net,   $10. OO 

This  is  undoubtedly  the  most  comprehensive 


SCIENTIFIC   PUBLICATIONS.  45 


work  on  a  rapidly  growing-  and  immensely  im- 
portant branch  of  engineering,  and  is  likely 
to  remain  for  long  the  standard  book  on  the 
subject. 

and    PARRY,    E.       Electrical    Equipment    of 

Tramways    In  Press. 

PASSMORE,     A.     €.       Handbook      of      Technical 

Terms  used  in  Architecture  and  Building,  and 
their  Allied  Trades  and  Subjects.  8vo,  cloth. 
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PATERSON,    D.,    F.C.S.      The    Color    Printing    of 

Carpet  Yarns.  A  useful  manual  for  color 
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illustrations.  8vo,  cloth,  illustrated,  net,  $3.50 

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colored  plate.  8vo,  cloth,  illustrated,  net,  $3.00 

PATTEN,  J.     A  Plan  for  Increasing;  the  Humidity 

of  the  Arid  Region  and  the  Utilization  of  Some 
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Power  and  other  Purposes.  A  paper  communi- 
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den,  Utah,  Sept.  12,  1903.  4to,  pamphlet,  20 
pp.,  with  7  maps  $1 . 00 

PATTON,  H.  B.  Lecture  Notes  on  Crystallog- 
raphy. Revised  Edition,  largely  rewritten. 
Prepared  for  use  of  the  students  at  the  Colo- 
rado School  of  Mines.  With  blank  pages  for 
note-taking.  8vo,  cloth  net,  $1.25 

PAULDING,   C.   P.      Practical   Laws   and  Data   on 

the  Condensation  of  Steam  in  Covered  and 
Bare  Pipes;  to  which  is  added  a  translation  of 
Peclet's  "Theory  and  Experiments  on  the 
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•  «.•«.«/<«*«..  < ««««  .net,  81.  *9 


46  D.   VAN    NOSTRAND   COMPANY'S 


PBIRCE,     B.       System     of     Analytic     Mechanics. 

4  to,     cloth     $10 . 00 

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PERRIGO,  O.  E.  Devices,  Change  Gear.  Show- 
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pitches  of  Threads.  Cloth  $1.00 

PERRINE,  F.  A.   C.,  A.M.,  D.Sc.      Conductors  for 

Electrical  Distribution:  their  Manufacture  and 
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PERRY,  J.     Applied  Mechanics.     A  Treatise   for 

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PHILLIPS,  J.  Engineering  Chemistry.  A  Prac- 
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students  and  others.  Comprising  methods  of 
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terials used  in  Engineering  works,  with  num- 
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larged. 8vo,  cloth  net,  $4.50 

Gold  Assaying.  A  Practical  Handbook  giv- 
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Chemical  Tests  required  in  the  Processes  of 
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PHIN,  J.      Seven  Follies   of   Science.     A  Popular 

Account  of  the  most  famous  scientific  impossi- 
bilities and  the  attempts  which  have  been 
made  to  solve  them;  to  which  is  added  a  small 
Budget  of  Interesting  Paradoxes,  Illusions 
and  Marvels.  With  numerous  illustrations. 
Second  Edition.  8vo,  cloth,  illustrated. 
net,  $1.25 

PICKWORTH,    C.    IV.      The    Indicator    Handbook. 

A  Practical  Manual  for  Engineers.  Part  I.  The 
Indicator:  its  Construction  and  Application. 
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PUBLICATIONS.  47 


'—The  Indicator  Handbook.      Part   II.     The  In- 

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gether with  Numerous  Rules  and  Practical 
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Engineer — Civil,  Mechanical  and  Electrical. 
Seventh  Edition.  12mo,  flexible  cloth,  $1.00 

PLANE  TABLE,  THE.  Its  Uses  in  Topographi- 
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$2.00 

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PLATTNER'S  Manual  of  Qualitative  and  Quan- 
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PLYMPTON,  Geo.  W.,  Prof.  The  Aneroid  Bar- 
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POCKET  LOGARITHMS,  to  Four  Places  of  Deci- 
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POPE,    F.    L.      Modern    Practice    of   the    Electric 

Telegraph..  A  Technical  Handbook  for  Elec- 
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POPPLEWELL,   W.   C.      Elementary   Treatise    on 

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cloth,     illustrated     $3.00 

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48  D.  VAN   NDSTfcAND 


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$1.50 

PRATT,  HERBERT.  Wiring  a  House.  Pamph- 
let   $0.25 

PRAY,  T.,  Jr.     Twenty  Years  with  the  Indicator: 

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PREECE,  W.  H.     Electric  Lamps In  Press. 

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PRELINI,  C.,  C.E.     Earth  and  Rock  Excavation. 

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PRESCOTT,    A.    B.,   Prof.      Organic   Analysis.      A 

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Quantitative  Analysis  of  Organic  Materials  in 
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SCIENTIFIC  PUBLICATIONS.  49 


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PRESS,  A.     Design  of  Electrical  Machinery.  8vo, 

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PRITCHARD,  O.  G.  The  Manufacture  of  Elec- 
tric-light Carbons.  Illustrated.  8vo,  paper. 
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industrial  products;  Part  II,  Metals;  Part  III, 
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PULLEN,    W.    W.     P.       Application     of    Graphic 

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With  diagrams  and  figures.  Translated  from 
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RANDAU,  P.  Enamels  and  Enamelling.  An  in- 
troduction to  the  preparation  and  application 
©f  all  kinds  of  enamels  for  technical  and  artis- 
tic purposes.  For  enamel-makers,  workers  in 
gold  and  silver,  and  manufacturers  of.  objects 
of  art.  Third  German  Edition.  Translated 
by  Charles  Salter.  With  figures,  diagrams  and 
tables.  SVQ,  cloth,  illustrated  net,  $4.00 

RANKINE,  W.  J.  M.  Applied  Mechanics.  Com- 
prising the  Principles  of  Statics  and  Cine- 
matics, and  Theory  of  Structures,  Mechanism, 
and  Machines.  With  numerous  diagrams.  Sev- 
enteenth Edition,  thoroughly  revised  by  W.  S. 
Millar.  8vo,  cloth  $5.00 

Civil  Engineering.      Comprising  Engineering 

Surveys,  Earthwork,  Foundations,  Masonry, 
Carpentry,  Metal-work,  Roads,  Railways, 
Canals,  Rivers,  Water-works,  Harbors,  etc. 
With  numerous  tables  and  illustrations. 
Twenty-first  Edition,  thoroughly  revised  by 
W.  J.  Millar.  8vo,  cloth  $6.50 

—Machinery    and    Millwork.       Comprising    the 

Geometry,  Motions,  Work,  Strength,  Construc- 
tion, and  Objects  of  Machines,  etc.  With  near- 
ly 300  woodcuts.  Seventh  Edition,  thoroughly 
revised  by  W.  J.  Millar.  8vo,  cloth  ..$5.00 


SCIENTIFIC   PUBLICATIONS.  51 


The   Steam-engine  and   Other   Prime   Movers. 

With  diagram  of  the  Mechanical  Properties  of 
Steam.  Folding  plates,  numerous  tables  and 
illustrations.  Fifteenth  Edition,  thoroughly 
revised  by  W.  J.  Millar.  8vo,  cloth  ....$5.00 

Useful   Rules  and   Tables   for  Engineers  and 

Others.  With  Appendix,  Tables,  Tests  and 
Formulae  for  the  use  of  Electrical  Engineers. 
Comprising  Submarine  Electrical  Engineering, 
Electric  Lighting  and  Transmission  of  Power. 
By  Andrew  Jamieson,  C.E.,  F.R.S.E.  Seventh 
Edition,  thoroughly  revised  by  W.  J.  Millar. 
8vo,  cloth  $4.00 

and    BAMBER,    E.    F.,    C.E.      A    Mechanical 

Text-book.  With  numerous  illustrations.  Fifth 
Edition.  8vo,  cloth $3.50 

RAPHAEL,  F.  C.  Localization  of  Faults  in  Elec- 
tric Light  and  Power  Mains,  with  chapters  on 
Insulation  Testing.  With  figures  and  dia- 
grams. Second  Edition,  revised.  8vo,  cloth, 
illustrated  net,  $3.00 

RATEAU,    A.      Experimental    Researches    on   the 

Flow  of  Steam  through  Nozzles  and  Orifices, 
to  which  is  added  a  note  on  the  Flow  of  Hot 
Water.  (Extrait  des  Annales  des  Mines,  Janu- 
ary, 1902.)  Authorized  translation  by  H.  Boyd 
Brydon.  With  figures,  tables,  and  folding 
plates.  8vo,  cloth,  illus net,  $1.50 

RAUTENSTRAUCH,  W.,  Prof.  Syllabus  of  Lec- 
tures and  Notes  on  the  Elements  of  Machine 
Design.  With  blank  pages  for  note-taking. 
8vot  cloth,  illustrated  net,  $1.50 

and  WILLIAMS,  J.  T.     Machine  Drafting  and 

Empirical  Design.     8vo,  cloth   In  Press. 

RAYMOND,  E.  B.  Alternating-current  Engin- 
eering Practically  Treated.  With  numerous 
diagrams  and  figures.  Second  Edition.  12mo, 
cloth  net,  $2 . 50 

RAYNER,    H.       Silk    Throwing    and    Waste    Silk 

Spinning.  With  numerous  diagrams  and  fig- 
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RECIPES  for  the  Color,  Paint,  Varnish,  Oil,  Soap 

and  Drysaltery  Trades.  Compiled  by  an  Ana- 
lytical Chemist.  8vo,  cloth  $3.50 

RECIPES   FOR  FLINT  GLASS   MAKING.      Being 

Leaves  from  the  mixing-book  of  several  ex- 
perts in  the  Flint  Glass  Trade.  Containing  up- 
to-date  recipes  and  valuable  information  as 
to  Crystal,  Demi-crystal,  and  Colored  Glass  in 


52  D.   VAN    NOSTRAND   COMPANY'S 


its  many  varieties.  It  contains  the  recipes  for 
cheap  metal  suited  to  pressing,  blowing,  etc., 
as  well  as  the  most  costly  Crystal  and  Ruby. 
British  manufacturers  have  kept  up  the  qual- 
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present  time.  The  book  also  contains  remarks 
as  to  the  result  of  the  metal  as  it  left  the  pots 
by  the  respective  metal  mixers,  taken  from 
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Compiled  by  a  British  Glass  Master  and  Mixer. 
12mo,  cloth  net,  $4.50 

REED'S  ENGINEERS*  HANDBOOK  to  the  Local 

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to  the  Elementary  Questions.  Illustrated  by 
358  diagrams  and  37  large  plates.  Seventeenth 
Edition,  revised  and  enlarged.  8vo,  cloth,  $5.00 

Key    to    the    Seventeenth    Edition    of    Reed's 

Engineers'  Handbook  to  the  Board  of  Trade 
Examination  for  First  and  Second  Class  En- 
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the  questions  given  in  the  examination  papers. 
By  W.  H.  Thorn.  8vo,  cloth $3.00 

Useful    Hints    to    Sea-going    Engineers,    and 

How  to  Repair  and  Avoid  "Breakdowns;"  also 
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plates.  Third  Edition,  revised  and  enlarged. 
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and  Prevention  of  their  Priming,  with  Re- 
marks on  their  General  Management.  12mo, 
cloth,  illustrated  $2 . 00 

REINHARDT,   C.   W.      Lettering    for   Draftsmen, 

Engineers,  and  Students.  A  Practical  System 
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$1.00 

REISER,  F.     Hardening  and  Tempering  of  Steel, 

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German  of  the  third  and  enlarged  edition.,  by 
Arthur  Morris  and  Herbert  Robsori.  8vo, 
cloth,  120  pages  $2 ,50 


SCIENTIFIC  PUBLICATIONS.  53 


— N.      Faults    in    the    Manufacture    of    Woolen 

Goods  and  their  Prevention.  Translated  from 
the  second  German  edition,  by  Arthur  Morris 
and  Herbert  Robson.  8vo,  cloth,  illustrated. 
net,  $2.50 

Spinning:     and     Weaving     Calculations     with 

special  reference  to  Woolen  Fabrics.  Trans- 
lated from  the  German  by  Chas.  Salter.  8vo, 
cloth,  illustrated  net,  $5.00 

RICE,  J.    M.,  and  JOHNSON,  W.  W.      On   a   New 

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tions, with  especial  reference  to  the  Newton- 
ian conception  of  Rates  or  Velocities.  12mo, 
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RICHARDS,  F.,  and  COLVIN,  F.  H.     Perspective, 

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RIDEAL,  S.,  D.Sc.     Glue  and  Glue  Testing,  with 

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RIPPER,  W.  A  Course  of  Instruction  in  Ma- 
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ROBERTS,  J.,  Jr.  Laboratory  Work  in  Electri- 
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ond Year  Students  of  Electrical  Engineering. 
With  Figures,  Diagrams  and  Tables.  8vo, 
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ROBERTSON,  L.  S.     Water-tuhe  Boilers.     Based 

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versity College,  London.  With  upward  of 
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ROBINSON,  J.  B.  A  New  System  of  Architectur- 
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with  additions.  16mo,  cloth,  illustrated.  (Van 
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ROEBLING,  J.  A.  Long  and  Short  Span  Rail- 
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ROLLINS,  W.  Notes  on  X-Lieht.  With  152  full- 
page  plates.  Svo.  cloth,  illustrated,  net,  $7.50 


54  D.    VAN    NOSTRAND    COMPANY'S 


ROSE],   .1.,   M.E.      The   Pattern -makers'   Assistant. 

Embracing  Lathe  Work,  Branch  Work,  Core 
Work,  Sweep  Work  and  Practical  Gear  Con- 
structions, the  Preparation  and  Use  of  Tools, 
together  with  a  large  collection  of  useful  and 
valuable  Tables.  Ninth  Edition.  With  250 
engravings.  8vo,  cloth  $2.50 

Key    to     Engines     and    Engine-running.       A 

Practical  Treatise  upon  the  Management  of 
Steam-engines  and  Boilers  for  the  use  of  those 
who  desire  to  pass  an  examination  to  take 
charge  of  an  engine  or  boiler.  With  numerous 
illustrations,  and  Instructions  upon  Engineers' 
Calculations,  Indicators,  Diagrams,  Engine 
Adjustments  and  other  Valuable  Information 
necessary  for  Engineers  and  Firemen.  12mo. 
cloth.  Illus $2.50 

ROUILLION,    LOUIS.      Cams.      The    Drafting    of. 

Pamphlet .$0.25 

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ing Hand  Work  in  the  Elementary  and  Sec- 
ondary Schools.  8vo,  cloth  $2.00 

ROWAN,    F.    J.      The    Practical    Physics    of    the 

Modern  Steam-boiler.  With  an  Introduction 
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lustrations and  diagrams.  8vo,  cloth,  illus- 
trated   $7.50 

SABINE,  R.  History  and  Progress  of  the  Elec- 
tric Telegraph.  With  descriptions  of  some  of 
the  apparatus.  Second  Edition,  with  additions. 
12mo,  cloth  $1.25 

SAEL.TZER,  A.  Treatise  on  Acoustics  in  Con- 
nection with  Ventilation.  12mo,  cloth,  $1.00 

SALOMONS,  Sir  D.,  M.A.  Electric-light  Installa- 
tions. A  Practical  Handbook.  With  numerous 
illustrations.  Vol.  I.,  The  Management  of  Ac- 
cumulators. Ninth  Edition,  revised  and  mostly 
rewritten.  12mo,  cloth  $1.50 

Vol.  II.  Seventh  Edition,  revised  and  enlarged, 
Apparatus.  296  illus.  12mo,  cloth $2.25 

Vol.  III.  Seventh  Edition,  revised  and  en- 
larged. Applications.  12mo  cloth  $1.50 

—Management    of   Accumulators.      A    Practical 

Handbook.  Ninth  Edition,  revised.  (An  edi- 
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L,ight  Installations  and  the  Management  of 
Accumulators.)  With  figures  and  plates. 
12mo,  cloth,  illustrated ..net,  $2.50 


SCIENTIFIC  PUBLICATIONS.  55 


SANFORD,  P.  G.     Nitro-explosives.     A  Practical 

Treatise  concerning  the  Properties,  Manufac- 
ture and  Analysis  of  Nitrated  Substances,  in- 
cluding- the  Fulminates,  Smokeless  Powders 
and  Celluloid.  Second  Edition,  revised  and 
enlarged.  8vo,  cloth  net,  $4.00 

SAUNDERS,  C.  H.  Handbook  of  Practical  Me- 
chanics for  use  in  the  Shop  and  Draughting- 
room;  containing  Tables,  Rules  and  Formulae, 
and  Solutions  of  Practical  Problems  by  Simple 
and  Quick  Methods.  16mo,  limp  cloth,  $1.00 

SAUXXIER,.   C.       Watchmaker's     Handbook.       A 

Workshop  Companion  for  those  engaged  in 
Watchmaking  and  allied  Mechanical  Arts. 
Translated  by  J.  Tripplin  and  E.  Rigg.  Sec- 
ond Edition,  revised,  with  appendix.  12mo. 
cloth  $3.50 

SCHELLEN,  H.,  Dr.     Magneto-electric  and  Dyna- 

mo-electrie  Machines:  their  Construction  and 
Practical  Application  to  Electric  Lighting,  and 
the  Transmission  of  Power.  Translated  from 
the  third  German  edition  by  N.  S.  Keith  and 
Percy  Neymann,  Ph.D.  With  very  large  ad- 
ditions and  notes  relating  to  American  Ma- 
chined, by  N.  S.  Keith.  Vol.  I,  with  353  illus- 
trations. Second  Edition.  8vo,  cloth,  $5.00 

SCHERER,     R.       Casein:      its     Preparation      and 

Technical  Utilization.  Translated  from  the 
German  by  Chas.  Salter.  8vo,  cloth,  illus- 
trated   net,  $3.00 

SCHMAL.L,,  C.  N.  First  Course  in  Analytic  Ge- 
ometry, Plane  and  Solid,  with  Numerous  Ex- 
amples. Containing  figures  and  diagrams. 
12mo,  half  leather,  illustrated net,  $1.75 

and  SHACK,  S.  M.  Elements  of  Plane  Ge- 
ometry. An  Elementary  Treatise.  With  many 
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SCHMEER,  Louis.  Flow  of  Water:  A  New  The- 
ory of  the  Motion  of  Water  under  Pressure, 
and  in  Open  Conduits  and  its  Practical  Appli- 
cation. Svo,  cloth,  illustrated  In  Press. 

SCHUMANN,  F.  A  Manual  of  Heating  and  Ven- 
tilation in  its  Practical  Application,  for  the 
use  of  Engineers  and  Architects.  Embracing  a 
Series  of  Tables  and  Formulae  for  Dimensions 
of  Heating,  Flow  and  Return  Pipes  for  Steam 
and  Hot-water  Boilers,  Flues,  etc.  12mo,  il- 
lustrated, full  roan  $1.50 


56  D.  VAN  NOSTRAND  COMPANY^ 


SCHWEIZER,  V.      Distillation   of  Resins,  Resin- 

ate  Lakes  and  Pigments;  Carbon  Pigments  and 
Pigments  for  Typewriting  Machines,  Manifold- 
ers,  etc.  A  description  of  the  proper  methods 
of  distilling  resin-oils,  the  manufacture  of 
resonates,  resin-varnishes,  resin-pigments  and 
enamel  paints,  the  preparation  of  all  kinds  of 
carbon  pigments,  and  printers'  ink,  litho- 
graphic inks  and  chalks,  and  also  inks  for 
typewriters,  manifolders,  and  rubber  stamps. 
With  tables  and  68  figures  and  diagrams.  8vo, 
cloth,  illustrated  net,  $3.50 

SCIENCE   SERIES,  The  Van  Nostrand.    (Follows 

end  of  this  list.) 

SCRIBNER,    J.    M.       Engineers'    and    Mechanics' 

Companion.  Comprising  United  States  Weights 
and  Measures,  Mensuration  of  Superfices  and 
Solids,  Tables  of  Squares  and  Cubes,  Square 
and  Cube  Roots,  Circumference  and  *Areas  of 
Circles,  the  Mechanical  Powers,  Centres  of 
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•Specific  Gravity  of  Bodies,  Strength,  Weight 
and  Crush  of  Materials,  Water-wheels,  Hydro- 
statics, Hydraulics,  Statics,  Centres  of  Per- 
cussion and  Gyration,  Friction  Heat,  Tables 
of  the  Weight  of  Metals,  Scantling,  etc.,  Steam 
and  Steam-engine.  Twenty-first  Edition,  re- 
vised. 16mo,  full  morocco  $1.50 

SEATON,  A.  E.  A  Manual  of  Marine  Engineer- 
ing. Comprising  the  Designing,  Construction 
and  Working  of  Marine  Machinery.  With 
numerous  tables  and  illustrations  reduced 
from  Working  Drawings.  Fifteenth  Edition, 
revised  throughout,  with  an  additional  chapter 
on  Water-tube  Boilers.  8vo,  cloth  $6.00 

and  ROUNTHWAITE,  H.  M.     A  Pocket-book 

of  Marine  Engineering  Rules  and  Tables.  For 
the  use  of  Marine  Engineers  and  Naval  Archi- 
tects, Designers,  Draughtsmen,  Superintend- 
ents and  all  engaged  in  the  design  and  con- 
struction of  Marine  Machinery,  Naval  and 
Mercantile.  Seventh  Edition,  revised  and  en- 
larged. Pocket  size.  Leather,  with  diagrams. 
$3.00 

SEIDELL,,   A.      (Bureau  of  Chemistry,  Wash.,  D. 

C.).  Solubilities  of  Inorganic  and  Organic 
Substances.  A  handbook  of  the  most  reliable 
Quantitative  Solubility  Determinations.  12mo, 
cloth,  367  pp.  net,  $3.00 

SEVER,  G.  F.,  Prof.  Electric  Engineering  Ex- 
periments and  Tests  on  Direct-current  Ma- 
chinery. With  diagrams  and  figures.  Second 


57 


edition,  revised  and  enlarged.  8vo  pamphlet, 
illustrated,  75  pp net,  $1.00 

and  TOWNSEND,  F.  Laboratory  and  Fac- 
tory Tests  in  Electrical  Engineering.  Second 
Edition,  revised  and  rewritten.  8vo,  cloth,  il- 
lustrated, 269  pp net,  $2.50 

SEWALL,,    C.    H.      Wireless    Telegraphy.      With 

diagrams  and  engravings.  Second  Edition, 
corrected.  8vo,  cloth,  illustrated  ...net,  $2.00 

Lessons  in  Telegraphy.  For  use  as  a  Text- 
book in  schools  and  colleges,  or  for  individual 
students.  Illustrated.  12mo,  cloth  $1.00 

SEWELL,,  T.  Elements  of  Electrical  Engineer- 
ing. A  First  Year's  Course  for  Students.  Sec- 
ond Edition,  revised,  with  additional  chapters 
on  Alternating-current  Working  and  Appen- 
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diagrams,  tables  and  examples.  8vo,  cloth,  il- 
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The    Construction    of   Dynamos    (Alternating 

and  Direct  Current).  A  text-book  for  students, 
engineer-constructors,  and  electricians-in- 
charge.  8vo,  cloth.,  illus.,  316  pp.  ..net,  $3.00 

SEXTON,  A.  H.  Fuel  and  Refractory  Materials. 
8vo,  cloth  $2 . 00 

Chemistry   of  the   Materials   of  Engineering. 

A  Handbook  for  Engineering  Students.  With 
tables,  diagrams  and  illustrations.  12mo, 
cloth,  illustrated  $2.50 

SEYMOUR,     A.       Practical     Lithography.       With 

figures  and  engravings.  8vo,  cloth,  illustrated. 
net,  $2.50 

SHAW,  P.   E.     A  First-year  Course   of  Practical 

Magnetism  and  Electricity.  Specially  adapted 
to  Ihe  wants  of  Technical  Students.  Inter- 
leaved for  note-taking.  8vo,  cloth,  illustrated. 
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S.  The  History  of  the  Staffordshire  Potter- 
ies, and  the  Rise  and  Progress  of  the  Manu- 
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erences to  genuine  specimens,  and  notices  of 
eminent  potters.  A  re-issue  of  the  original 
work  published  in  1829.  8vo,  cloth,  illustrated. 
net,  $3.00 

Chemistry  of  the  Several  Natural  and  Arti- 
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ufacturing Porcelain,  Glass  and  Pottery.  Re- 
issued in  its  original  form,  published  in  1837. 
8vo,  cloth  net,  $5.00 


58  D.  VAN   NOSTfcAND  COMPANY'S 

SHELDON,  S.,  Ph.D.,  and  MASON,  H.,  B.S.  Dy- 
namo-electric Machinery:  its  Construction,  De- 
sign and  Operation,  Direct-current  Machines. 
Sixth  Edition,  revised.  8vo,  cloth,  illustrated. 
net,  92 .50 

——Alternating-current      Machines:      being      the 

second  volume  of  the  author's  "Dynamo-elec- 
tric Machinery:  its  Construction,  Design  and 
Operation."  With  many  diagrams  and  figures. 
(Binding  uniform  with  volume  I.)  Fifth  Edi- 
tion. 8vo,  cloth,  illustrated net,  92.50 

SHIELDS,  J.  E.  Notes  on  Engineering  Con- 
struction. Embracing  Discussions  of  the  Prin- 
ciples involved,  and  Descriptions  of  the  Ma- 
terial employed  in  Tunneling,  Bridging,  Canal 
and  Road  Building,  etc.  12mo,  cloth  ...91.50 

SHOCK,    W.    H.      Steam    Boilers:    their    Design, 

Construction  and  Management.  4to,  half  mo- 
rocco   915 . 00 

SHREVE,   S.  H.      A  Treatise   on  the   Strength   of 

Bridges  and  Roofs.  Comprising  the  determin- 
ation of  algebraic  formulas  for  strains  in 
Horizontal,  Inclined  or  Rafter,  Triangular, 
Bow-string,  Lenticular  and  other  Trusses, 
from  fixed  and  moving  loads,  with  practical 
applications  and  examples,  for  the  use  of 
Students  and  Engineers.  87  woodcut  illustra- 
tions. Fourth  Edition.  8vo,  cloth  93.50 

SHUNK,  W.  F.      The  Field  Engineer.      A   Handy 

Book  of  practice  in  the  Survey,  Location  and 
Track-work  of  Railroads,  containing  a  large 
collection  of  Rules  and  Tables,  original  and 
selected,  applicable  to  both  the  Standard  and 
Narrow  Gauge,  and  prepared  with  special  ref- 
erence to  the  wants  of  the  young  engineer. 
Eighteenth  Edition,  revised  and  enlarged. 
With  addenda.  12mo,  morocco,  tucks  ...92.50 

SIMMS,  F.  W.     A  Treatise  on  the  Principles  and 

Practice  of  Leveling.  Showing  its  application 
to  purposes  of  Railway  Engineering,  and  the 
Construction  of  Roads,  etc.  Revised  and  cor- 
rected, with  the  addition  of  Mr.  Laws'  Practi- 
cal Examples  for  setting  out  Railway  Curves. 
Illustrated.  8vo,  cloth  92.50 

Practical    Tunnel  inf.      Fourth    Edition.    Re- 
vised  ana  greatly   extended.     With  additional 

chapters  illustrating  recent  practice  by  D. 
Kinnear  Clark.  With  36  plates  and  other  il- 
lustrations. Imperial  8vo,  cloth  98.00 


SCIENTIFIC   PUBLICATIONS.  59 


SIMPSON,   G.      The   Naval   Constructor.      A   Vade 

Mecum  of  Ship  Design,  for  Students,  Naval 
Architects,  Ship  Builders  and  Owners,  Marine 
Superintendents,  Engineers  and  Draughtsmen. 
12mo,  morocco,  illustrated.  500  pages,  net,  $5.00 

SINCLAIR,  ANGUS.,  Mem.  Am.  Soc.  Mech.  Eng'rs. 

Development  of  the  Locomotive  Engine.  Be- 
ing- a  history  of  the  growth  of  the  locomotive 
from  the  most  elemental  forms,  with  biograph- 
ical sketches  of  the  eminent  engineers  and 
inventors.  Half  leather $5.00 

SINDALL,  R.  W.     Paper  Technology.     8vo,  cloth, 

158    illus.,    253    pp net,    $4.00 

SLATER,  J.  W.      Sewage  Treatment,  Purification 

and  Utilization.  A  Practical  Manual  for  the 
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SMITH,  F.  E.     Handbook  of  General   Instruction 

for  Mechanics.  Rules  and  formulae  for  prac- 
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1.   W.,  C.  E.      The  Theory   of  Deflections  and 

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ments of  Railway  Tracks.  Illustrated.  16mo, 
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tricity to  Mining  Work.  Second  Edition.  8vo, 
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SNOW,    W.    G    and    NOLAN,    T.       Ventilation     of 

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60  D.    VAN    NOSTRAND   COMPANY'S 


SOTHERN,  J.  W.     The  Marine  Steam  Turbine.     A 

practical  description  of  the  Parsons  Steam 
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run,  including  a  description  of  the  Denny  and 
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ond Edition.  8vo,  cloth,  illus.,  163  pp.  ..$2.50 

SOXIILET,   D.   H.      Art    of   Dyeing    and    Staining: 

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Wood,  and  of  imitating  all  sorts  of  Wood.  A 
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SPANG,  H.  W.  A  Practical  Treatise  on  Light- 
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SPEYERS,  C.  L..  Text -book  of  Physical  Chem- 
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STAL.EY,  C.,  and  PIERSON,  G.  S.     The  Separate 

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STEWART,    A.      Modern    Polyphase    Machinery. 

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SCIENTIFIC  PUBLICATIONS.  61 


Text-book  of  Magnetism  and  Electricity.  160 

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STILES,  A.  Tables  for  Field  Engineers.  De- 
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STILLMAN,  P.      Steam-engine   Indicator  and  the 

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STODOLA,    Dr.    A.       Steam    Turbines.      With    an 

appendix  on  Gas  Turbines,  and  the  future  of 
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Louis  *C.  Loewenstein  (Lehigh  University). 
With  241  cuts  and  3  lithographed  tables.  8vo, 
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STONE,  HERBERT,  F.L.S.,  F.R.C.I.     The  Timbers 

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STONEY,  B.  D.  The  Theory  of  Stresses  in  Gir- 
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SUFFICING,  E.  R.     Treatise  on  the  Art  of  Glass 

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SWEET,  S.  H.     Special  Report  on  Coal,  Showing 

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SWOOPE,  C.  W.  Practical  Lessons  in  Electric- 
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62  D.    VAN    NOSTRAND   COMPANY'S 


TAIL.FER,  L,.  Practical  Treatise  on  the  Bleach- 
ing of  Linen  and  Cotton  Yarn  and  Fabrics. 
With  tables  and  diagrams.  Translated  from 
the  French  by  John  Geddes  Mclntosh.  8vo, 
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TEMPLETON,     W.       The      Practical      Mechanic's 

Workshop  Companion.  Comprising  a  great 
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of  practical  data  and  calculated  results  facili- 
tating mechanical  operations.  Revised  and 
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THOM,  C.,  and  JONES,  W.  H.  Telegraphic  Con- 
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THOMAS,    C.    W.      Paper-makers'    Handbook.      A 

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THOMPSON,  A.  B.     Oil  Fields  of  Russia  and  the 

Russian  Petroleum  Industry.  A  Practical 
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— Roentgen  Rays  and  Phenomena  of  the  Anode 

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W.  P.  Handbook  of  Patent  L,aw  of  All 

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THORNL.EY,  T.  Cotton  Comhing  Machines. 
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SCIENTIFIC  PUBLICATIONS.  63 


THURSO,   J.   W.      Modern    Turbine    Practice    and 

Water-Power  Plants.  With  eighty-eight  fig- 
ures and  diagrams.  8vo,  cloth,  illustrated. 
Second  Edition,  revised  net,  $4.00 

TINNEY,     W.     H.       Gold-mining    Machinery;    its 

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agers and  Engineers.  With  a  chapter  on  the 
Preparation  of  Estimates  of  Cost.  8vo,  cloth, 
illustrated,  308  pp net,  $5.00 

TITHERLEY,   PROF.   A.   W.      Laboratory   Course 

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TOCH,  M.     Chemistry  and  Technology  of  Mixed 

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TODD,   J.,   and   WHALL,   W.    B.      Practical    Sea- 

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TOMPKINS,  A.  E.  Text-book  of  Marine  Engin- 
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TOOTHED    GEARING.      A    Practical    Handbook 

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TRINKS,  W.,  and  HOUSUM,  C.     Shaft  Governors, 

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TUCKER,  J.  H.,  Dr.  A  Manual  of  Sugar  Analy- 
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Analytical  Methods  to  the  Sugar  Industry. 
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Cane-Sugar,  Dextrose,  Levulose,  and  Milk- 
Sugar.  Sixth  Edition.  8vo,  cloth,  illus.  ..$3.50 

TUMLIRZ,  O.,  Dr.     Potential  and  Its  Application 

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TUNNER,    P.    A.      Treatise    on    Roll-turning    for 

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SCIENTIFIC   PUBLICATIONS.  65 


Year  Book  of  Mechanical  Engineering;  Data. 

With  many  tables  and  diagrams.  (First  year 
of  issue  1907.)  In  Press. 

VAN    WAGENEN,    T.    F.      Manual    of    Hydraulic 

Mining.  For  the  Use  of  the  Practical  Miner. 
Revised  and  enlarged  edition.  18mo,  cloth. 
$1.00 

VEGA,    VON     (Baron).      Logarithmic    Tables    of 

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W.  L.  F.  Fischer,  M.A.,  F.R.S.  Eighty-first 
Edition.  8vo,  half  morocco  $2.50 

VILLON,     A.      M.        Practical     Treatise     on     the 

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Frank  T.  Addyman,  B.Sc.  8vo,  cloth,  illus- 
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VINCENT,     C.       Ammonia     and     its     Compounds: 

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VOLK,    C.       Haulage    and    Winding    Appliances 

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VON    GEORGIEVICS,    G.      Chemical    Technology 

of  Textile  Fibres:  their  Origin,  Structure, 
Preparation,  Washing,  Bleaching,  Dyeing, 
Printing,  and  Dressing.  Translated  from  the 
German  by  Charles  Salter.  With  many  dia- 
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306    pages     net,    $4.50 

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—Chemistry    of    Dyestuffs.      Translated    from 

the  Second  German  edition  by  Chas.  Salter. 
8vo,  cloth,  412  pages  net,  $4.50 

WABNER,  R.     Ventilation  in  Mines.     Translated 

from  the  German  by  Charles  Salter.  With 
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240  pages  net,  $4.50 

WADE,  E.  J.  Secondary  Batteries:  their  The- 
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66  D.    VAN    NOSTRAND   COMPANY'S 


WALKER,  F.,  C.E.  Aerial  Navigation.  A  Prac- 
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SYDNEY    P.,    M.I.E.E.,    Assoc.    M.I.C.E.,    &c., 

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W.   H.      Screw   Propulsion.      Notes   on    Screw 

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WALLIS-TAYLER,  A.  J.  Bearings  and  Lubrica- 
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—Modern     Cycles,    a    Practical     Handbook     on 

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SCIENTIFIC  PUBLICATIONS.  67 


Refrigerating  and  Ice-making  Machinery.     A 

Descriptive  Treatise  for  the  use  of  persons 
employing  refrigerating  and  ice-making  in- 
stallations, and  others.  8vo,  cloth,  illus.,  $3.00 

Refrigeration     and     Cold     Storage:     being     a 

Complete  practical  treatise  on  the  art  and 
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grams and  figures.  8vo,  cloth net,  $4.50 

Sugar    Machinery.      A    Descriptive    Treatise, 

devoted  to  the  Machinery  and  Apparatus  used 
in  the  Manufacture  of  Cane  and  Beet  Sugars, 
12mo,  cloth,  illustrated  $2.00 

WANKLYN,  J.   A.      A   Practical   Treatise   on   the 

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Foye.  Fourth  edition,  revised  and  en- 
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Jghn  P.  Wisser. 

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George  J.  Specht,  Prof.  A.  S.  Hardy,  John  B. 
McMaster,  and  H.  F.  Walling.  Third  Edition, 
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bra  of  Algebraic  Numbers.  By  Prof.  Wil- 
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No.  80.  HEALTHY  FOUNDATIONS  FOR 

Houses.      By   Glenn   Brown. 

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Browne. 

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the  Use  of  Antiseptics.  By  Samuel  Bagster 
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Henry  S.  H.   Shaw,  C.E. 

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The  Theoretical  and  Practical  Training  nec- 
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gated  Mathematically.  By  Dr.  G.  S.  Ohm, 
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Civil  and  Mechanical  Engineers.  Compiled 
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Distribution  of  Power  from  Central  Stations 
by  Compressed  Air.  By  Prof.  W.  C.  Unwin. 
Edited  by  F.  E.  Idell.  Third  edition. 

No.   107.  A   GRAPHICAL   METHOD   FOR    SWING 

Bridges..  A  Rational  and  Easy  Graphical 
Analysis  of  the  Stresses  in  Ordinary  Swing- 
Bridges.  With  an  Introduction  on  the  Gen- 
eral Theory  of  Graphical  Statics,  with  Fold- 
ing Plates.  Second  edition.  By  Benjamin  F. 
La  Rue. 

No.   108.   SLIDE-VALVE   DIAGRAMS.      A   French 

Method  for  Constructing  Slide-valve  Dia- 
grams. By  Lloyd  Bankson,  B.S.,  Assistant 
Naval  Constructor,  U.  S.  Navy.  8  Folding 
Plates. 

No.  109.  THE  MEASUREMENT  OF  ELECTRIC 

Currents.  Electrical  Measuring  Instruments. 
By  James  Swinburne.  Meters  for  Electrical 
Energy.  By  C.  H.  Wordmgham.  Edited, 
with  Preface,  by  T.  Commerford  Martin. 
With  Folding  Plate  and  Numerous  Illustra- 
tions. 

No.  110.  TRANSITION    CURVES.      A    Field-book 

for  Engineers,  Containing  Rules  and  Tables 
for  Laying  out  Transition  Curves.  By  Wal- 
ter G.  Fox,  C.E.  Second  edition. 

No.   111.   GAS-LIGHTING      AND      GAS-FITTING. 

Specifications  and  Rules  for  Gas-piping. 
Notes  on  the  Advantages  of  Gas  for  Cook- 
ing and  Heating,  and  Useful  Hints  to  Gas 
Consumers.  Third  edition.  By  Wm.  Paul 
Gerhard,  C.E. 

No.   112.  A    PRIMER    ON    THE    CALCULUS.      By 

E.  Sherman  Gould,  M.  Am.  Soc.  C.  E.     Third 
edition,   revised  and  enlarged. 

No.  113.  PHYSICAL  PROBLEMS  and  Their  So- 
lution. By  A.  Bourgougnon,  formerly  As- 
sistant at  Bellevue  Hospital.  Second  ed. 

No.   114.  USE       OF       THE       SLIDE       RULE.       By 

F.  A.    Halsey,   of   the    "American   Machinist." 
Fourth  edition,  revised  and  enlarged. 


THE)    VAN    NOSTRAND    SCIENCE    SERIES. 


No.  115.  TRAVERSE  TABLE.  Showing  the  Dif- 
ference of  Latitude  and  Departure  for  Dis- 
tances Between  1  and  100  and  for  Angles  to 
Quarter  Degrees  Between  1  Degree  and  90 
Degrees.  (Reprinted  from  Scribner's  Pocket 
Table  Book.) 

No.  116.  WORM  AND  SPIRAL,  GEARING.  Re- 
printed from  "American  Machinist."  By  F. 
A.  Halsey.  Second  revised  and  enlarged 
edition. 

No.   117.  PRACTICAL        HYDROSTATICS,       AND 

Hydrostatic  Formulas.  With  Numerous  Il- 
lustrative Figures  and  Numerical  Examples. 
By  E.  Sherman  Gould. 

No.   118.   TREATMENT     OF     SEPTIC     SEWAGE, 

with  Diagrams  and  Figures.  By  Geo.  W. 
Rafter. 

No.   119.   LAY-OUT  OF  CORLISS  VALVE  GEARS. 

With  Folding  Plates  and  Diagrams.  By 
Sanford  A.  Moss,  M.S.,  Ph.D.  Reprinted 
from  "The  American  Machinist,"  with  revi- 
sions and  additions.  Second  edition. 

No.  120.  ART  OF  GENERATING  GEAR  TEETH, 

By  Howard  A.  Coombs.  With  Figures,  Dia- 
grams and  Folding  Plates.  Reprinted  from 
the  "American  Machinist." 

No.   121.  ELEMENTS      OF      GAS      ENGINE      DE- 

sign.  Reprint  of  a  Set  of  Notes  accompany- 
ing a  Course  of  Lectures  delivered  at  Cor- 
nell University  in  1902.  By  Sanford  A. 
Moss.  Illustrated. 

No.   122.   SHAFT    GOVERNORS.       By    W.    Trlnks 

and   C.    Housum.      Illustrated. 

No.  123.  FURNACE  DRAFT:  ITS  PRODUCTION 

by  Mechanical  Methods.  A  Handy  Reference 
Book,  with  figures  and  tables.  By  William 
Wallace  Christie.  Illustrated.  Second  edi- 
tion, revised. 


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